JT presentation bridge: literature audit before the next attack

6 September 2026 · Research assessment requested before further attack

The current work is a reconstruction of known geometric amplitudes in a restricted chamber, with an explicit contact-prescription ambiguity. The audit found a closer precedent for the reconstruction argument than the first note credited. It has not established new physical dynamics, a direct BF derivation, or the novelty of the remaining forest/polytope formula.

There is a precise outstanding derivation in the selected source. Its importance should be judged by whether solving it identifies the gravitational measure or an observable that an incomplete presentation misses. A new way to reproduce a total volume would be a more limited result.

1. The closest prior work changes the attribution

Anagnostou–Mullane–Norbury, Weil-Petersson volumes, stability conditions and wall-crossing, arXiv:2310.13281v1, §4.2, Lemma 4.4, does more than give the zero-boundary-length formula used as our control. Its proof combines vanishing at a soft face, the dilaton relation, symmetry, and a polynomial-degree bound to determine the remaining polynomial uniquely. The same strategy recurs in §4.3. Primary text

Our argument with two arbitrary geodesic boundary lengths uses zero values and first normal derivatives of the difference on every defect face. It is appropriately described as an adaptation of that interpolation strategy. The predecessor was located during this audit; this is retrospective attribution of methodological precedent, not a claim that the earlier derivation consciously followed it.

The general-boundary forest formula was not located verbatim in the sources checked. That limited negative search result does not establish novelty. In particular, a different notation or a standard intersection-theoretic specialization may already contain it.

2. Assessment of each component

The mathematical proofs and rational checks in the first packet remain as recorded. This research step did not independently re-prove every statement or provide external review.

3. The precise open derivation

Wei Gu’s Conical Defects in JT Gravity from BF Theory: Quantization, Fusion, and Weighted Moduli Spaces, submitted 3 September 2026, explicitly imports the global weighted Weil–Petersson class in §4.7. Section 4.7.1 gives a BF sewing interpretation of the string identity, but uses the geometric forgetful map to integrate the compactified moving marked point. It leaves a direct BF Ward derivation of boundary and collision terms open, together with higher Virasoro constraints. Primary text, §4.7.1, submission record

Thus the known target is a derivation of already specified amplitudes. It is not a source claiming that extra propagating dynamics have been overlooked. A successful derivation could still matter: it could identify which global integration data and collision prescriptions the local gauge description requires. Extending it to physically distinct observables would be an additional accomplishment.

Eberhardt–Turiaci, 2D dilaton gravity and the Weil–Petersson volumes with conical defects, arXiv:2304.14948v2, supplies the weighted class and geometric relations. Its §5.1 already performs localization for disk configurations with collidable defects, using the geometric class. Consequently, a new localization calculation must identify the missing gauge-theory measure or prescription; invoking localization by itself is not a new bridge. Primary text

The source-free insertion is a normalized moving marking, not simply the instruction to delete a vertex from a fixed configuration. An attempted Ward derivation must respect that distinction.

4. Symmetry can hide physical information, but that issue is already studied here

Blommaert–Mertens–Verschelde, Fine Structure of Jackiw-Teitelboim Quantum Gravity, arXiv:1812.00918v3 (20 September 2019), distinguishes local classical BF equivalence from a quantum integration prescription. It discusses the hyperbolic component of flat connections, Teichmüller versus mapping-class-quotiented integration, and boundary constraints. It also treats horizon edge states and factorization. Its positive-subsemigroup formulation is a specific construction, not a license to replace the gravitational integration space by unrestricted BF connections. Primary text, introduction and §§3–5

Donnelly–Freidel’s Local subsystems in gauge theory and gravity gives an earlier general framework in which boundary variables support gauge-invariant surface charges. It distinguishes gauge transformations from physical surface symmetries. Primary text

These sources support the user’s underlying question: an incomplete reduction can omit boundary information. They also show that “restore edge modes” is not by itself an unexplored JT target. We need to name the map, the retained boundary data, and an observable whose treatment is deficient. No such new deficiency has yet been established by our scalar reconstruction.

Witten’s Matrix Models and Deformations of JT Gravity, arXiv:2006.13414v1, introduction, explicitly explains that products of exponential defect insertions need a contact prescription and that changing the prescription changes the correspondence between classical couplings and quantum amplitudes. Primary text

Our parameterized contact term is an explicit diagnostic of this familiar issue. A coupling reparametrization must be compared with the operators and sources transformed consistently. Differences at fixed, uncalibrated source labels do not automatically mean two different physical theories.

5. What an alternative presentation can usefully accomplish

Budd–Meeusen–Zonneveld, A tree bijection for the moduli space of genus-0 hyperbolic surfaces with boundaries, submitted 10 December 2025, constructs a tree representation, identifies the Weil–Petersson Poisson structure and measure, and extracts a geodesic-distance-difference statistic among three cusps. Theorem 5 gives the associated distance-dependent three-point function. This provides a concrete comparison: a presentation can transport a metric observable as well as a partition function. Primary text, §§1.1, 3, 5, submission record

Its cusp/geodesic-boundary sector differs from our collidable-cone sector. It is neither a proof of our desired BF map nor a newly selected research target.

The Losev–Manin space is already a permutohedral toric variety. This is reviewed and generalized by da Rosa–Jensen–Ranganathan in Toric graph associahedra and compactifications of M(0,n). Primary text

Postnikov’s Permutohedra, associahedra, and beyond develops volume formulas for Minkowski sums and graphical zonotopes, including tree/forest combinatorics. These are relevant antecedents for our convex-volume representation. Author’s paper

These precedents do not identify our particular weighted BF symplectic form with a toric form. They do mean that even a geometric moment-polytope interpretation could be standard toric geometry. The nontrivial bridge would have to start with the specified gravitational gauge theory and carry its measure and operator insertions through the reduction.

6. A bounded next attack, with a stopping criterion

Retain JT as a conditional presentation-bridge investigation, not as evidence that a new quantum-gravity effect is close. Do not resume an amplitude census or add more defect orders.

The next decisive question is:

With the gravitational integration cycle, boundary state, normalized defect operator, and contact-renormalization prescription explicitly fixed, does the gauge theory determine the measure at a two-defect collision and its soft boundary terms, or is the proposed determination still importing the weighted geometric class?

The known benchmark in our conventions is

$$V_2(b_1,b_2;q,p)=\frac{b_1^2+b_2^2}{2}+4\pi^2qp, \qquad q,p>0,\quad q+p<1.$$

This formula is a control, not the hoped-for new result. The test must determine why the stated prescription produces its measure and excludes the soft-invisible contact alternatives. Setting a counterterm to zero by convention or assuming the desired degree bound does not answer that question.

A successful first step must exhibit a gauge-theory Ward or reduction mechanism with a credible extension to arbitrary insertion number. Only then should the uniform degree question be resumed. A two-defect numerical match alone is insufficient. If the calculation remains prescription-dependent, identify the invariant content of that dependence and stop the route unless a specific new observable survives it.

For any claim of previously omitted dynamics, additionally require an observable and its algebra or evolution that cannot be removed by a consistently transformed source/field redefinition. We have not met that requirement.

7. Decision and research limits

The original choice has a better structural form than the withdrawn combinatorial target: it asks for an exact translation. However, the audit materially lowers the novelty assessment of what we have already done. The current evidence supports a useful working note and one tightly specified derivation test. It does not support a Publication or a claim that unconsidered dynamics have been found.

Checked primary texts include the particular sections linked above, the current JT proof packet, and its stated dependencies. Targeted searches also checked Losev–Manin/permutohedral and forest-volume precedents. This is not an exhaustive priority search across every equivalent notation, and no researcher was contacted. Newly identified methodological precedents are credited retrospectively; they are not misrepresented as sources consciously used in the first attack.

Selfridge remains paused. The semicomplete-digraph target remains withdrawn. The tree-bijection paper is a comparison, and the previously retained horizon alternative is still unselected.