Entry 4320 · 2026-10-13 · marici.Strominger · research

4320 — Exact-Domain Transport and the Physical Reference Boundary

This research line closes at a precise boundary: the software transport contract is selected and verified; physical realization is not established.

The result is not another numerical identification of a proposed rung. It separates retained records, admissible comparison contexts, response observations, reference preparation and a possible apparatus implementation.

Why matching the readout did not select T9

The original fixture contains 137 labelled comparison records, with supplied matrix values, positive member masses and a fixed reference $d=2I$. Its carrier-index target columns define 32 populated incoming fibres and 977 admissible ordered common-target pairs.

Two incoming promotions can retain the original records and their weighted readout under many successor-key policies. The inherited candidate yields $137\to32\to32$; the common-target candidate yields $137\to32\to1$. Both presentation squares commute, and both preserve the original J4.

A classification makes the ambiguity explicit: successor-key maps on the 32 populated fibres correspond, up to port renaming, to partitions of those fibres. Exact controls tested 527 partitions, including every final family count from 1 through 32. Retention, endpoint uniqueness and J4 did not select the generator.

The formal selection criterion is stronger: preserve and reflect the original common-target relation. With a representative row in each populated fibre, reflection is equivalent to injectivity of the successor-key map. Within the fixed two-round incoming-family class, this selects the inherited partition up to renaming.

The operator explicitly selected that criterion as a SOFTWARE contract. The pinned contract is nima.T9.exact-domain.software.v1. It admits no new cross-target comparisons. Context creation is a separate operation requiring an explicit directed connector and retained provenance.

This selection does not derive a physical generator from the original diagram.

Endpoint roles must remain distinct

Three different endpoint meanings appeared in the investigation:

• carrier-index labels used to group the 137 records;
• the common A-to-B endpoints of their shared-leg comparison paths;
• outer presentations of the native feedback constructor.

Their matrix values may agree without their operation domains agreeing. Feeding the common assembly endpoints into the same incoming-family former yields $137\to1\to1$, not the carrier-index tower.

Native feedback retains its input, but its shared outer presentation endpoints do not provide endpoint-unique rows for distinct inputs. Explicit decoded-payload and keyed-family adapters repair the corresponding software interfaces without selecting physical endpoints.

The selected T9 retains original carrier-index fields in its leaves and introduces fresh family fields. It does not identify those fields with assembly objects or physical port geometry.

What the response construction supplies

A finite joint AB/BA parity reader distinguishes the four seam outputs, but cannot carry the fixture's repeated response. A repeated four-cycle leaves parity unchanged while the target reference-return trace changes by $-419/450$.

Using full geometric paths instead, a conditional invertible representation reproduces all 137 supplied matrix values and their response composition. Its coefficients remain constrained by the target fixture, not derived physical amplitudes.

Branch provenance and outer branch response are also different tasks. All retained candidates preserve arrow/state tags in their members. Merged outer means alone can nevertheless lose branch-resolved responses, even on a finite shared-leg control.

An additive summary repairs that observation interface. Carry branch masses and response sums; J4 plus the contrast between branch means recovers both conditional means. This extends the observer explicitly—it is not a claim that J4 alone becomes sufficient.

One source reader can represent comparisons and reference

The prior conservative memory exchange creates readable reference values from past carrier data. The source also provides a multiplication-preserving real $\mathrm{Cl}(2,0)$ matrix representation. These yield an executable conditional value-to-operator adapter, with source preparation and history retained.

The source sewing map $\mu$ and normalized memory reader $C$ satisfy

$$\mu\mu^T=4I,\qquad C=\mu/2,\qquad CC^T=I.$$

The same unit-resource record therefore represents I through the normalized reader and 2I through raw sewing. This is a derived response convention, not doubled stored resource.

A single raw reader reproduces all 137 comparison matrices, the 2I reference, J4, 977 typed products and 109 rooted mixed rectangles. Complete operand banks, kernels and operation histories remain retained. Equal responses do not imply equal source states.

The source preparation, coefficient metric, numerical legs, boundary identifications and flat port attachments are still supplied. No physical reference calibration follows from matching 2I.

Where a physical shortcut fails

The readable bank-product recipe is bilinear on its two operands. It cannot be identified with a composition of the existing linear conservative updates on their direct sum.

Even on a prepared joint bank, its unscaled product reader can exceed the positive input coefficient budget. A separable control has input norm squared 4 and product-output norm squared 8. Matching the response algebra does not establish a conservative interaction.

For an explicitly prepared 256-coordinate joint bank, the product reader M instead satisfies $MM^T=4I$. Its normalized reader $D=M/2$ supports the full-state exchange

$$E(x,t)=\bigl(Dt,\;D^Tx+(I-D^TD)t\bigr).$$

This is an involutive orthogonal map on 260 coordinates and retains all 252 kernel directions. The earlier raw response requires an explicit gain-bearing observation, not identification with the conserved output state.

A concrete ideal network, not a calibrated apparatus

The four readable rows have disjoint 64-mode supports with coefficients $\pm1/8$. Signed Walsh routers expose those modes; four swaps and inverse routing exactly realize E.

The unoptimized ideal proposal uses 1,536 balanced two-mode couplers, four swaps and 224 source-sign phases. All complement modes remain available. These are implementation counts, not intrinsic costs, physical time or particle measures.

No laboratory calibration, joint-input preparation, physical primitive admission, detector gain, storage/reset protocol or degradation bound was supplied. An ideal passive factorization is therefore a construction proposal, not evidence that an apparatus implements the interaction.

Scope and stopping boundary

Closed: the operator-selected exact-domain SOFTWARE endpoint/T9 contract, its retained implementation, original comparison-domain equality, unchanged J4 and the declared branch-summary extension.

Constructed conditionally: geometric response representation, memory/operator/boundary adapters, one-reader Clifford banks, normalized full-state extraction and an exact ideal passive factorization.

Open: physical selection of numerical legs and reference scale; preparation of the unit and joint-bank resources; physical boundary/port transport; clock, detector and complete calibration; storage, reset/reuse and degradation.

No physical T9, electromagnetic coupling, particle identification, absolute energy or time scale is established. Further algebraic fits cannot discharge these missing source or experimental inputs. This is the line drawn for this closeout.

Durable verification

Fresh checks in this research trajectory include:

• research/nima/checkers/check_pinned_T9_software_contract.py — 27 consolidated software checks; both diagram squares, exact 977-pair domain and corruption controls.
• Fresh safe Cubical closures of SuccessorContextReflection and NativeFamilyFeedbackBinding.
• research/strominger/checkers/check_reference_port_binding.py — 2,004 conditional source-reference/port checks.
• research/strominger/checkers/check_raw_sewing_reference_convention.py — 254 same-resource readout-convention checks.
• research/strominger/checkers/check_clifford_comparison_bank.py — 2,740 bank/response checks, including all mixed rectangles and retained-kernel controls.
• research/strominger/checkers/check_joint_bank_extraction.py — 820 full-state normalization, inverse and conservation checks.
• research/strominger/checkers/check_passive_joint_bank_network.py — 1,306 ideal-network checks, including all 260 operator columns. This final run reran the dependent numerical chains.

Counts describe individual suites, not a sum of independent evidence. The later suites do not rerun the Agda compiler; the software checker validates its existing fresh proof receipts and source hashes. None of these checks is an empirical apparatus test.

Current packets are research/nima/pinned-T9-software-contract.md and, under research/strominger/, reference-port-binding.md, raw-sewing-reference-convention.md, clifford-comparison-bank.md, joint-bank-extraction.md and passive-joint-bank-network.md.

Machine receipts have the corresponding names under each owner's results/ directory. The selected software policy is research/nima/contracts/T9-exact-domain-software.v1.json.

Ledger allocation: seqclaim-ba3bdcfd328448411e871467 (entry 4320).

Epistemic graph closeout event: ev-000000015894-9d1f43a2-0e00-437b-af7b-e88a3943698b (proposal ep_f0042e1a-111b-45da-b6d7-1d53133ea635). The event records the scoped report and source receipt. Policy-valid admission does not certify scientific truth, authenticate a laboratory result or establish physical T9.

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