H2 Acceptance Report

Issue: sci-dug.3
Date: June 7, 2026
Gate: 02 H2 metric reconstruction from pulse comparisons

Verdict

H2 is accepted at the ideal fixed-event level and partially accepted at the finite-data prototype level.

Accepted:

• ideal fixed-event uniqueness of the Lorentzian metric under the reviewed assumptions
• separation of metric uniqueness from event-manifold identification
• finite pulse-record schema for practical records
• first executable finite-data slices for Minkowski, weak-static, stationary direction timing, Shapiro-style spatial delay, and weak-wave differential arm timing, with the Shapiro and weak-wave slices treated as calibrated response benchmarks rather than full raw-record schema implementations
• finite-data gauge and stability conditions for restricted ansatz fits, with first-slice uncertainty propagation demonstrated in code
• sufficient raw-relational conditions for promoting event graphs to fixed-event inputs

Not accepted:

• general reconstruction of an arbitrary metric from sparse finite records
• automatic raw-relational derivation of the smooth event manifold, clock embeddings, or proof-grade signal directions for arbitrary records
• practical metric reconstruction without a stated ansatz, gauge convention, calibration model, and nuisance model

Artifacts

Proof and schema:

• H2 fixed-event theorem
• H2 finite pulse-record schema
• H2 finite-data stability and gauge conditions
• H2 raw relational identifiability
• Roadmap

Code:

• src/pulse_model/h2_reconstruction.py

Executable checks:

• tests/test_h2_reconstruction.py

Accepted Ideal Result

The ideal H2 theorem proves the following bounded statement:

Given a fixed smooth event region, incidence map, embedded clock segments, proof-grade signal directions or infinitesimal signal curves, dense null-rich signal data, clock-rich timelike samples, calibrated universal clocks, and a compatible Lorentzian metric, no second compatible Lorentzian metric exists on that fixed-event realization.

The proof strategy is:

• signal directions determine the null cone
• null cones determine the conformal metric class
• calibrated pulse-derived timelike durations fix the conformal factor
• coordinate freedom remains as diffeomorphism gauge

This is enough to make $[g_{\mu\nu}]$ the right ideal H2 target.

The raw-relational appendix states sufficient conditions under which event graphs can supply the fixed-event inputs. It is not a proof that arbitrary raw pulse records automatically produce the event manifold or signal tangent directions.

Accepted Finite Prototype Result

The finite-data work is accepted only as a restricted prototype.

Implemented slices:

Slice	Accepted result	Gauge or ansatz
Minkowski static clocks	Equal pulse-derived clock rates recover the flat static-clock slice	Reference-clock time-scale gauge
Weak static field	Clock ratios recover potential differences	Reference clock fixes additive potential convention
Stationary direction timing	Counter-propagating signal times recover a signed timing asymmetry	Observable asymmetry, not unique coordinate $g_{0i}$
Spatial delay	Shapiro-style benchmark records recover a $\gamma$ proxy	Calibrated endpoint geometry and mass model supplied as interpretation metadata
Weak wave	Differential arm timing benchmark records recover injected $h_+$	Fixed arm geometry, polarization basis, and long-wavelength approximation supplied as interpretation metadata

The prototype demonstrates that selected pulse/signal-style records and calibrated response benchmarks can recover selected metric-response parameters with explicit tolerances and uncertainty propagation. It does not yet reconstruct a general metric field or implement the full finite schema for every slice.

Stability And Gauge Decision

Finite H2 stability is accepted only under the conditions in the stability appendix:

• the metric or response ansatz is stated
• gauge choices are stated
• nuisance variables are fixed, bounded, or jointly estimated
• the residual and covariance model are stated
• the gauge-fixed Jacobian or equivalent sensitivity calculation is full rank for the claimed parameters
• uncertainty propagation is reported
• known degeneracies are named

The current executable prototype satisfies the first-slice gauge conventions and closed-form uncertainty propagation checks. It does not yet satisfy the full Jacobian/covariance stability program for arbitrary finite networks, all nuisance parameters, or full metric-field reconstruction.

Remaining Assumptions

H2 still depends on:

• clock universality after calibration
• signal propagation by the relevant null structure
• correct signal-link labels
• controlled environmental clock shifts
• enough clock and signal richness for the claimed ansatz
• explicit gauge fixing
• correct nuisance modeling
• finite-data sensitivity above numerical and measurement noise floors
• raw-relational event and signal identifiability conditions for claims beyond fixed-event reconstruction

H3 Start Decision

H3 can safely start, with a boundary.

H3 may use the ideal fixed-event H2 result as a metric equivalence-class input:

$$[g_{\mu\nu}]$$

It may also use the finite prototype outputs as toy or ansatz-level reconstructed metric-response data.

H3 must not assume that H2 has already solved raw-relational event-manifold identification or arbitrary sparse finite-data metric reconstruction. The first H3 task should define a loop observable against a fixed-event or explicitly gauge-fixed reconstructed metric object, then state which parts depend on later H2 strengthening.

Gate Decision

The 02 H2 metric reconstruction from pulse comparisons gate is:

• accepted for the ideal fixed-event uniqueness theorem
• partially accepted for finite-data reconstruction prototypes under stated ansatz and gauge conditions, with full finite-data stability still conditional
• conditional for raw-relational identifiability under the sufficient conditions in the appendix
• not accepted for arbitrary sparse-record metric reconstruction

This is sufficient to unblock the first H3 loop-observable work, provided H3 keeps the fixed-event and gauge boundaries explicit.