Pith Number

pith:DUW46IQR

pith:2026:DUW46IQRRA2A3K4WA2ELCKTKHV

not attested not anchored not stored refs pending

First Law of Proto-Area Entropy from Modular Spectral Geometry

Ling-Zheng Xia, Lixin Xu

arxiv:2607.29432 v1 · 2026-07-31 · hep-th · gr-qc · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DUW46IQRRA2A3K4WA2ELCKTKHV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-08-03T01:34:20.798838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d2dcf221188340dab960688b12a6a3d574bd394a5c0879348fba3aac81cdafa

Aliases

arxiv: 2607.29432 · arxiv_version: 2607.29432v1 · doi: 10.48550/arxiv.2607.29432 · pith_short_12: DUW46IQRRA2A · pith_short_16: DUW46IQRRA2A3K4W · pith_short_8: DUW46IQR

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/DUW46IQRRA2A3K4WA2ELCKTKHV \
  | 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: 1d2dcf221188340dab960688b12a6a3d574bd394a5c0879348fba3aac81cdafa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f046f3ea11e6d69e55c521c48430bfaafa829bd4a7e1ad84bb3bf847c34760f3",
    "cross_cats_sorted": [
      "gr-qc",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-07-31T13:55:16Z",
    "title_canon_sha256": "31dc3aa2d0f6b5d981423473a27553ceee7f73877d4410b501dcd11627815e20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29432",
    "kind": "arxiv",
    "version": 1
  }
}