Pith Number

pith:P62JI5YF

pith:2026:P62JI5YFAMRONEOLZ7JUFO3VYA

not attested not anchored not stored refs pending

The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity

Daniel L. Jafferis, Diandian Wang

A restricted open Virasoro TQFT computes 3d gravitational path integrals on compact regions, using fixed-length boundary conditions above the black hole threshold and fixed-angle conditions below it.

arxiv:2604.09396 v2 · 2026-04-10 · hep-th · gr-qc

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\usepackage{pith}
\pithnumber{P62JI5YFAMRONEOLZ7JUFO3VYA}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that it computes gravitational path integrals on compact regions with fixed-length boundary conditions for states above the black hole threshold, and fixed-angle boundary conditions for states below the threshold.

C2weakest assumption

The restriction of the full open-closed Virasoro TQFT to a subclass of admissible manifolds accurately captures the open sector of a CFT ensemble and yields the stated gravitational path integrals.

C3one line summary

Open Virasoro TQFT computes 3d gravity path integrals on compact regions using threshold-dependent boundary conditions and yields an open-closed duality relating Conformal Turaev-Viro theory to the diagonal sector of two Virasoro TQFT copies.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-14T01:20:58.485601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fb49477050322e691cbcfd342bb75c025a78ad19ce5638edd32db0908ea4185

Aliases

arxiv: 2604.09396 · arxiv_version: 2604.09396v2 · doi: 10.48550/arxiv.2604.09396 · pith_short_12: P62JI5YFAMRO · pith_short_16: P62JI5YFAMRONEOL · pith_short_8: P62JI5YF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/P62JI5YFAMRONEOLZ7JUFO3VYA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7fb49477050322e691cbcfd342bb75c025a78ad19ce5638edd32db0908ea4185

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b142ec34a5fe27a05487354f919af138fdd407bee921d0206adc1e25cb2ccde0",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-04-10T15:10:03Z",
    "title_canon_sha256": "ba11eff9686d52394910d86b11658d0e7b869b5d77a9677b36c0a49de9e6a8c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.09396",
    "kind": "arxiv",
    "version": 2
  }
}