Fax cost is a joint
optimization problem.

The container compresses original bytes, records a digest, optionally encrypts the payload, and applies Reed–Solomon protection with interleaving. Layouts include visible grid cells, MH code-tree run lengths and shifted halftone dot clusters. A compatible receiver or browser decoder reconstructs the original file, including its original color and graphics, selectable text and document structure. A conventional fax machine prints the encoded raster; the decoder recovers the PDF. Encoded pages are off by default, need the recipient’s agreement, and are compared with ordinary and packed pages for each attempt; where prices are comparable they are selected only for a lower estimated bill. In development, decoding also accepts the forms real receivers return, such as a test line’s PDF receipt, Group 3 and Group 4 images, pages stored in strips, inverted or upside-down pages and an added header line, refuses a page drawn again at another size with one sentence saying what to decode instead, and the browser decoder reads the new capacity layout.

The ordinary 30-page fax used 10,630,416 image-data bits with the smaller of measured MH and MMR encodings. The run-coded page used 484,704 MH bits: 1,328,802 → 60,588 bytes, a 95.44% reduction (about 22× smaller). All three layouts recovered the exact original PDF after Group 4 TIFF storage and rereading. The 55,422-byte source and 37,382-byte container are intermediate sizes. This offline text-document benchmark measures image payload; call overhead and carrier charges are separate. On 9 October 2026, one encoded page sent through Telnyx to HumbleFax recovered the exact 55,422-byte PDF from the provider’s received file. Telnyx reported $0.01 for that call and for its comparison call, so the pair showed no monetary saving, and one carrier path is not a general interoperability claim. Dense layouts require an exact-raster path and observed ECM/fine-resolution support. The development decoder is proven with synthetic fixtures; no encoded page has yet been decoded from a real third-party receipt.

The constrained-channel model assigns different costs to fax code bits and the pixels consumed by run lengths. A cost-weighted run distribution moves the optimum between temporal efficiency and page density. The experimental enumerative profile already maps payload bits into MH patterns with a bounded code-bit cost and is used only when you select it. In development, the capacity layout draws the payload as runs with an arithmetic coder over frozen frequency tables for the complete T.4 code, in time, pages and balanced profiles; for a recipient whose decoder you recorded as reading it, the layout chooser prices the time and pages profiles and the route’s bill decides. It exploits the legal code alphabet and source distribution; it does not compress arbitrary encrypted data beyond its entropy.

Measured on full fine pages of random payload in MH at 14,400 bit/s, the time profile carries a kilobyte in 0.663 seconds, 4% less than the best run-coded run-length limit for time and 7% less than the default, while the pages profile carries 357 kB a page, 14% more than the best run-coded limit for pages and 55% more than the default. These are encoder measurements, not call timings, and they fall well short of the modeled capacity bound, which left out each line’s offset, check bits and padding. On a live call through Telnyx to HumbleFax on 9 October 2026, the enumerative page used 397,944 measured JBIG bits against 420,576 for the run-coded page of the same document (5.38% fewer); both calls were billed the same. Capacity pages need a decoder recorded as reading them, and a partner’s signed capabilities do not yet state which layouts its decoder reads.

Before each attempt on Faxbot’s own engines, the layout chooser measures MH, MR, MMR and JBIG on that attempt’s prepared pages, with JBIG measured as the SSL Fax engine sends it, and prices each layout with the smallest coding the call may use. Faxbot asks for MR and MMR only when the receiving machine’s capabilities allow them and for JBIG only when a call has put those capabilities on record, and MMR and JBIG always go with error correction. A coding that failed twice in a row to a number is not used for it again. In development, the same measurements are made for every account a fax may use before the account is chosen, so an account that is cheaper once its pages are coded is no longer ranked on raw page counts.

On synthetic pages, MH came out 20% smaller than MMR on a shaded table, 30% on a tinted form and 34% on a noisy gray scan, while MMR was about half the size of MH on black text. In the SSL Fax engine loopback, three shaded pages took 58 seconds of transfer in JBIG and 108 in MH. No live call has used a measured coding yet. Encoded page data is only part of the wire cost: framing, fill, error correction, retransmissions and negotiation also count, and the coding can still change during negotiation.

Choose each row’s one-dimensional or two-dimensional encoding under the reset-spacing constraint. Each two-dimensional row references the preceding raster row regardless of how that row was encoded. Dynamic programming finds the legal schedule with the lowest cost after byte alignment and minimum scanline fill. The SSL Fax engine sends every MR page with that schedule, computed from each row’s measured codes and the bytes the engine actually emits, including its end-of-line alignment. It is on by default with a switch for each recipient, and a tuned page a machine refuses makes later calls to that number plain for that coding, with no resend.

Without scanline fill, fixed MR used 1,487,193 bytes and tuned MR 1,178,491. Adding tuned MR to the best previous non-JBIG comparison reduced 1,186,913 to 1,113,161 bytes, winning on 8/20 files. Against fixed MR, 18-byte and 72-byte minimum line fill reduce the gains to 15.19% and 5.77%. Independent reconstruction recovered every original raster; 1,980 small schedules matched exhaustive enumeration. Faxbot’s MR measurement matches the engine byte for byte on the corpus and at image build. The engine tuning is proven at image build and in synthetic tests only: the loopback run is still in progress, no real receiver has taken a tuned page, and the built-in engine still codes MR on its fixed schedule. These are encoder measurements, not complete call timings.

The SSL Fax engine sends each JBIG page with the smallest of 12 T.85 settings, covering typical prediction, the two-line template and moved adaptive-template pixels. Tuned JBIG goes only where the receiving machine is known to decode it: pages over SSL Fax, an enrolled partner whose signed statement says its own Faxbot answers, or a number you enabled with its warning, because a receiving machine confirms a JBIG page before decoding it. Further research searches when and where the adaptive template changes, charging the signaling overhead as well as the image data. This makes encoder configuration part of document optimization.

The tinted form fell from 29,003 to 5,629 bytes; the corpus from 594,970 to 442,307. All 960 encoder/decoder comparisons recovered identical pixels. The corpus has 19 unique rasters and a median reduction of 0.258%; gains are concentrated in particular page types. Per-page search adds 2.11% beyond the improved fixed preset. The engine tuning is proven at image build and in synthetic tests only; no real receiver has taken a tuned page yet. Search over adaptive-template decision timing remains research.

An ECM partial-page block holds up to 256 frames, each carrying 64 or 256 octets of fax image data. Crossing a block boundary introduces another control exchange; crossing a page boundary introduces a different exchange. Dense pages already stack whole original pages onto long fax pages within the length the receiving machine accepts, removing end-of-page exchanges where the route’s billing says it saves. In development, the cutter shares pages among the same number of long pages so that the fewest cross a 64 KiB partial-page boundary, and the predictor adds an estimated turnaround for each extra block. Packing should therefore price encoded bytes, block counts and page transitions together, while respecting document order and fidelity.

Dense pages are proven with synthetic pages and session logs; no packed page has gone over a real call yet. The per-block turnaround is a fixed estimate of about 3.3 seconds; observed timing on one gateway is not a universal acknowledgement cost. The joint cutter, encoder and protocol-state objective remains research. Negotiated frame size, speed, error behavior and the carrier’s rounding rules determine the useful boundary.

The protected-region method freezes text, edges and other protected pixels, then changes suitable uniform shading interiors. Faxbot keeps a 4-pixel band around every change of gray, every pure black or white pixel, the PDF’s own text and annotations and the gaps between marks exactly as rendered, and draws only the inside of shaded areas at least 25 pixels wide and 8 rows tall with horizontal stripes. A fidelity check compares each changed page with the original, one kind of content at a time, and a page that would lose anything goes unchanged. Fax-friendly screening avoids the expensive alternating runs produced by conventional halftones. The objective is the resulting fax encoding, not just visual smoothness.

The recorded h16 screen reduced table MMR payload from 873,336 to 364,880 bits and form payload from 736,160 to 178,176 bits. Against each original’s smallest measured MH/MR/MMR encoding, the reductions are 47.77% and 65.47%. On Faxbot’s synthetic benchmark pages at 14,400 bit/s with error correction, the shipped screen takes the shaded table from 61 to 27 seconds and the tinted form from 51 to 13. Text/edge protection stayed intact; permitted background pixels changed. By default the screen applies only where it lowers the expected bill; making light areas white is a separate opt-in that can erase pale marks, and a recipient’s own choice of never always wins. Exact-record workflows can turn it off and use the lossless encoding path. No screened page has gone over a real call or through a cloud provider yet.

Recipient-approved case packets reference accepted documents. Each case document carries its source, version and purpose, and becomes acknowledged only through a partner’s signed receipt, the receiving team’s acknowledgement, a received acknowledgement fax or a person’s note; an acknowledgement expires after that recipient’s reuse period. Conceptually the task is to transmit X given receiver knowledge K: the new information plus authenticated identity, version and repair overhead.

For an illustrative packet with 100 accepted history pages and five new pages, the reference index adds one page: 105 pages become six, not five. Reuse is specific to the recipient and case, requires agreement, and must recover when the retained base is missing or expired; a recipient who could not find a document receives it in full next time. Fax acceptance does not establish chart filing or retention. Tested with synthetic data; no real recipient has acknowledged a packet yet.

Register a content-addressed background and rendering specification. Exchange the agreed version and field values, then compare exact reconstructed page hashes before filing. Faxbot draws the pages itself with a shipped font and its own text rendering, so the same form, values and renderer version produce the same dots on any computer. The receiver performs deterministic rendering rather than inferring or summarizing the form’s meaning.

Both partners need the agreed immutable template and a compatible renderer; a receiving Faxbot that lacks the form fetches it once. A version or page-hash mismatch blocks filing, and the full pages go by fax only when you choose. Tested with synthetic forms and two synthetic installations; not yet exchanged between two live installations.

Original-file reuse and bounded binary deltas send an enrolled partner only what it lacks: a reference to a document it already holds, or the changes from the case-document version it holds. Faxbot also stores each fax-image page’s body apart from the header band Faxbot generated, so a new header can travel without the body when the partner confirms, signed, that it still holds that body. Reconstruction checks the complete intended document or raster digest.

Only headers Faxbot generated are separated; arbitrary dates, signatures or annotations are not assumed disposable. Keeping each body apart makes every fax image about 3% larger on a dense page and up to 11% on a light one. Receiver authorization, an exact retained base and a missing-base repair path are required, and any miss sends the whole document at once. The measured example reduces bytes on a partner path that already avoids a carrier call; it is not another independently avoided call. Not yet run between two live installations.

A signed common-intake agreement names the exact fax numbers the receiving organization handles. Both administrators approve the coverage. The shared payload keeps a separate delivery identity, receipt and work item for every intended recipient, and the intake files each recipient’s copy only when that recipient’s own delivery arrives.

A shared company name, brand or email domain does not establish consent to consolidate. One shared transfer must not collapse distinct recipient obligations into a single success flag. Tested with two synthetic installations; no real partner intake has used it yet.

A deterministic checklist selects unchanged source documents against recorded recipient requirements and acceptance history. Preview included, referenced and missing material before sending. Approved manifests can identify shared evidence without treating every new submission as an entirely new chart. In development, an ordinary fax can drop its separate cover sheet: you set one line of notice text for the organization or a mailbox, Faxbot prints it at the top of every page, and a sender can mark the first page as a cover whose notice moves into that line so the page is not sent. A recipient marked as needing a cover sheet always receives it, and case packets, forms and faxes from email or folders are sent as they are.

Checklist selection and version-aware case history are implemented and tested with synthetic data. The recipient’s actual requirements and permission to reference earlier documents remain inputs; suggestions for missing items stay off unless you turn them on, and a model must not silently summarize away required evidence. The header notice is tested with synthetic documents; Faxbot never removes a page by itself and refuses a fax rather than send it without the notice.

For enrolled partners, signed custody checks establish which pages or document pieces arrived intact, only the remainder goes directly, and the receiver assembles and verifies the complete document once. For an ordinary recipient, you can send only the pages a broken call did not confirm, as a new fax that names the one it continues, when the call’s own record proves which pages arrived. Only a person sends it, and the original failed attempt remains in the history.

The ten-page example is illustrative. A lost response is not evidence of a missing page. Partner custody and an ordinary sender’s page counter provide different assurances; a route whose provider reports no page count offers only a full resend, and uncertain outcomes are reconciled before another transmission. No live call has been broken on purpose to test it yet.

Stable client operation identities recover an already accepted job after a timeout. Immutable attempt and provider bindings preserve transport history independently. Partner reconciliation and custody queries determine whether a receiver durably accepted the original even when its receipt was lost. A sent fax whose outcome cannot be confirmed becomes owned work: Faxbot runs the free checks first, closes the item itself when delivery is confirmed after all, and otherwise leaves the decision to a person.

Client idempotency, transport reconciliation, partner custody and repair are implemented and tested with synthetic faxes and a stand-in partner; the partner question has not yet run against a real partner. Neither retrying an API call nor receiving an SMTP acceptance establishes human acknowledgement.

Current routing combines rate cards, destination reliability and observed all-attempt cost per delivered fax, and a shared predictor prices each route from the prepared document’s measured pages and the account’s plan state. In development, Faxbot measures and prices every way each permitted account could send the pages before choosing the account, ranks accounts on that best measured price, and binds the chosen account to exactly the pages it was priced on. Selection stays inside the allowed provider, mailbox, endpoint and delivery-policy boundaries.

Observed charges, estimates and settlement are kept separate. Charged failures count; unknown cost is not zero. Route choice by cost per delivered fax is proven with synthetic data only, because no live number has two metered routes yet. The measured account choice is checked against a brute-force oracle on synthetic accounts with invented rates; no live fax has gone that way yet. The broader stochastic transaction model extends the implemented empirical routing rule rather than claiming an omniscient optimizer.

When a plan has only a few included pages or minutes left, the allocator compares permitted paid alternatives across the waiting queue and gives the allowance to whole faxes by what each would pay on its best other route. With 100 included pages and two eligible 100-page jobs, assigning the allowance to the expensive alternative leaves $0.50 payable instead of $50. A historical-demand reserve protects part of the remaining allowance for likely future jobs only when earlier periods show, at a 95% lower bound, that it would save more. The allocation changes only which route a fax takes.

The example is a reproduced synthetic allocation problem, not a customer saving. Exact small-queue solutions, a bounded fallback and historical-demand reservation are implemented, proven against every assignment of small synthetic queues and a replay of five synthetic months; nothing has run against a real plan month yet. The monthly subscription fee remains payable; a broader stochastic optimizer remains research.

Apply the contract’s unit, minimum and increment separately to each attempt. Couple document and duration estimates to those discontinuities: reducing 70 seconds to 61 can leave the bill unchanged, while a smaller reduction across the minute boundary changes the charged units. Faxbot prices each call by its expected bill over the learned spread of its duration, so a call equally likely to take 59 or 61 seconds bills 90 seconds expected on 60-second steps. In development, on a trunk billed in steps of 60 seconds or more, a built-in engine call on which no fax machine answers ends 50 seconds after answer instead of 60, so a person who stays on the line costs one minute, not two.

Rate-card rounding, charge reconciliation and expected-bill pricing are implemented; prepared-document pricing is tested with synthetic pages. The 61-to-59 example assumes a one-minute minimum and whole-minute increments, excluding any other fixed fees. The 50-second cap still waits longer than T.30’s 35 ± 5-second T1 timer for a fax machine to identify itself, and is proven in a loopback between two Faxbot fax engines, not yet against a real carrier.

Recipient-approved batching uses a bounded wait, a page cap and sender-mixing policy. Each document retains its confirmed-page outcome and allocated charge share. Urgent sends can bypass the wait, and separators are included in the page count and cost estimate. A recipient that agrees can take one index page or a line above every page instead of a separator before each document, saving N−1 or N pages per shared call. In development, waiting faxes are grouped into the calls that cost least in all, exactly for up to ten faxes, and a shared call can use long pages when the receiving machine accepts them.

Batching requires recipient agreement. A partial or uncertain shared call does not automatically authorize retransmitting every document in the batch. Shared calls are proven with synthetic faxes and over a local T.38 test line; a live combined call is still pending.

Call measurements record negotiated behavior, and the built-in engine records the far machine’s capabilities and training on every call. For each number, Faxbot starts at the speed that worked after repeated training failures, asks for T.38 at once where a number switches late, sends audio fax where only T.38 failed, and forgets what it learned when the trunk settings or an engine build change. Internet Aware Fax is used only for fax servers you approve. In development, route families keep failures caused by a shared route change out of per-number lessons and rank an account with an open route problem after reliable ones, and keys you saved for a phone menu are pressed after answer before the fax starts. Separate T.38 relay, G.711 passthrough, SSL Fax and Internet Aware Fax; they are not interchangeable capabilities.

Measurements and reliability history are implemented. The per-number memory has run only on synthetic call histories and in the loopback lab, and the rule that changes coding and error correction for a number stays unconfirmed until live calls show it. Route families are tested on replayed synthetic histories and keys after answer in a loopback against a stand-in menu. A registered SIP account does not prove that UDPTL can cross the network or that the carrier will accept T.38.

Current scheduling enforces destination concurrency, trunk channels and carrier call-rate limits. Uncertain calls keep their reservation until settled. Faxbot learns each number’s busy, unanswered and slow hours from recent calls, considers whether a failed try may be charged, and protects urgent work and deadlines. In development, power-aware sending reads a UPS through Network UPS Tools and, on battery, starts a trunk call only when the fax’s 90th-percentile call time fits the remaining runtime, otherwise preferring an approved route in another power domain. The research extension lets a cooperating receiver issue authenticated, expiring capacity grants and reserves room for legacy callers.

Local capacity scheduling and learned timing are implemented and tested on synthetic call histories, not yet on live traffic. Power-aware sending is tested against a stand-in UPS server. Cooperative receiver grants remain research; a capacity grant is permission to attempt delivery, not a document-acceptance receipt.

Exchange a minimal business envelope before the document: intended recipient, purpose, class, version and required acceptance conditions. A receiver can reject an incompatible submission before the expensive transfer or identify the missing requirement that would make it acceptable. Enrolled partners already exchange a signed preflight before a large transfer, in which the receiver can refuse early with its reason, such as sender, recipient, type, size, page count or freshness. Before a first fax, Faxbot warns when the NPI registry lists the number for a different provider. In development, the built-in engine compares the station a number answers as with the number dialed and its earlier stations before any page, and can hang up instead; a recipient that accepts instructions only from a registered number is pinned to the trunk, caller ID and station ID registered with it.

The signed partner preflight and the registry check are implemented; the station check is proven in loopback and registered senders with synthetic faxes. The general business-envelope protocol remains research. Transport preflight, station identity and endpoint reachability do not establish administrative or clinical acceptance, and Faxbot never changes a caller ID to match a registration.

Verified Faxbot partners exchange encrypted original PDFs, exact fax images and signed durable-acceptance receipts using familiar fax numbers, and a fax to one of your own receiving numbers arrives with no call. Configured Direct messaging accounts and FHIR R4 DocumentReference delivery add further routes, with conditional creation and uncertain-outcome lookup. For a partner whose intake is a fax server, a fax call can run directly between the two fax engines inside a WireGuard tunnel you set up.

Direct peers require enrollment and number binding. Direct/FHIR routes require configured trust and confirmed recipient endpoints and are proven against simulated services only; that does not establish a native EHR chart-filing integration. Reconcile an uncertain digital outcome before fax fallback.

The fax engine can use an existing carrier or PBX connection while other accounts handle receiving or additional outbound routes. Several accounts, a second account at one provider, several trunks and sites expose different contract, capacity and media-path choices without binding every direction to one provider. In development, an analog line behind a supported gateway becomes a flat-rate local route priced from its local calling area, and carrier presets cover trunks that carry encrypted fax only as audio.

Existing Asterisk and optional HylaFAX+ paths have different protocol capabilities. Multiple accounts and trunks are tested with synthetic data, not yet with two real accounts at one provider, and the gateway presets have not run against a real gateway. Price the account’s actual calls and fixed costs; an advertised wholesale rate is not the organization’s effective delivered-fax price, and a line without an entered price stays unpriced, never free.

Rate cards hold prices by where calls start and by number prefix, state-based US prices can favor one site’s trunk, approved toll-free alternatives are dialed only with the recipient’s recorded agreement, and T.30 polling lets the site whose calls are cheaper place the call. In development, carrier price decks that depend on the caller ID a call presents apply only to caller IDs you confirmed with evidence; a dialing guard allows your own country and destinations you already use, holds other faxes for approval, never dials premium-rate or satellite numbers unless you allow that kind, and can cap the price a minute; UAE and Saudi service rules are shown as unconfirmed until you confirm a provider’s licence, without blocking any fax; and an NTT Hikari Denwa preset prices Japan’s Data Connect by the bandwidth held. Compare setup, occupied time, access terms, media compatibility and destination eligibility together.

Only genuine authorized origins and permitted routes qualify; Faxbot never changes a caller ID to reach a cheaper rate. Prices a carrier does not publish stay unknown, never zero. The caller-ID prices and dialing guard are tested with synthetic decks and numbers. The NTT preset is built from NTT’s published documents, its detailed interface is not published, and it has not run against NTT. No universal tariff saving is implied.

Current advice compares monthly plans with metered alternatives, identifies quiet numbers, receiving pools and trunks whose faxes fit on another, and records number moves with their dependencies and retirement evidence. In development, a line inventory is matched to carrier discontinuance lists by wire center and to contract end dates, French sites show their copper closure dates from the published commune schedule, and call records imported from another fax server show the channels actually needed at peak.

The $3,000 figure is arithmetic, not a measured customer result. A line is removable only after checking seasonal, emergency, broadband and other dependencies; alarm, elevator and emergency lines stay out of the retirement plan because they need their own replacement. Advice does not cancel a carrier account or assume that zero recent calls proves zero future demand. The development imports are tested with synthetic files; AT&T’s published workbook was read in full, but no customer inventory has been used.

Email and watched-folder connectors bring existing applications and scanner workflows into the same import and sending paths, handling each document once. In development, Faxbot lists what copier makers document for network fax, gives SBC presets for running Faxbot as the fax annex behind Microsoft Teams Direct Routing, prepares one page for a fax server’s renewal with the channels needed at peak and the numbers still to move, and works out what taking the fax lines out of a POTS-replacement quote removes. Taking a copier’s network fax call and sending it on through Faxbot’s routing is still proposed.

Specific copier dialects, number splits and POTS-replacement dependencies need integration. Removing fax traffic saves equipment cost only when the associated port, license or replacement hardware is actually avoidable. The development pages are advice only and tested with synthetic files; none has run against a real copier, SBC, fax server or quote.

Receiving advice replays call history to compare shared capacity and metered arrangements, names the account where each number would cost least with the steps to move it, and chooses a reply number among your cheapest receiving numbers. On the SIP trunk, listed junk callers are declined before answer, so the call is never answered and no fax arrives to triage. Distinguish a carrier-side rejection from an answered call that already incurred a charge.

Capacity must account for blocked demand and the contract’s overflow behavior. Caller screening, selected reply numbers and portability depend on supported carriers, trusted signaling and explicit policy; they are not automatic changes to every installation. Receiving advice and screening are tested with synthetic calls and stand-in carriers.

Acquired-document provenance, owned queues, acknowledgement targets and evidence export are implemented. Expected faxes record obligations before arrival, distinguish strong references from tentative matches, and support outage reconciliation by sorting the next export into already done, new and held items.

An expected document must come from an entered or imported expectation. Weak matches need review. SMTP acceptance, fax success, owner acknowledgement and completion remain separate events; an outage ledger does not guarantee exactly-once action in another system. Tested with synthetic data; not yet run against a real ERP, EHR or partner.

Reprice the last 90 days of faxes, by recipient, along the best route Faxbot may use and again with exactly one more fact established, such as enrolling a partner Faxbot found, confirming a Direct address or FHIR endpoint, recording what a fax machine accepts or approving a toll-free number. A read-only setup portfolio planner then compares affordable groups of setup items under a spending limit, counts shared setup once, and returns both an expected and a cautious plan.

These are what past faxes would have cost, never savings. Each fact is priced on its own, and related facts that unlock the same route are not independent savings. A missing approval is a boundary, never an allowed route. The comparison prices the accounts Faxbot’s automatic choice may use rather than replaying your historical sending rules, so treat its ranking as a configuration lead. Portfolio plans are modeled, not measured savings; both are tested with synthetic installations.