Pith Number

pith:YC5WZ7MR

pith:1999:YC5WZ7MRZUCTF2CIXT422V5DNO

not attested not anchored not stored refs pending

Maximum Principles for Null Hypersurfaces and Null Splitting Theorems

Gregory J. Galloway

arxiv:math/9909158 v1 · 1999-09-27 · math.DG · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YC5WZ7MRZUCTF2CIXT422V5DNO}

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.

Cited by

1 paper in Pith

Thermodynamics of dynamical black holes beyond perturbation theory

Receipt and verification

First computed	2026-05-18T01:38:22.359890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0bb6cfd91cd0532e848bcf9ad57a36b9c04fe56b6b124917acd9e057bfdeda0

Aliases

arxiv: math/9909158 · arxiv_version: math/9909158v1 · doi: 10.48550/arxiv.math/9909158 · pith_short_12: YC5WZ7MRZUCT · pith_short_16: YC5WZ7MRZUCTF2CI · pith_short_8: YC5WZ7MR

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/YC5WZ7MRZUCTF2CIXT422V5DNO \
  | 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: c0bb6cfd91cd0532e848bcf9ad57a36b9c04fe56b6b124917acd9e057bfdeda0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbbff0d3b54e8b61fada6517c3fdf37373ad77ca9426fb3414028c00da77047c",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1999-09-27T14:04:58Z",
    "title_canon_sha256": "b8614676a79c6f6f1fe442f3cb7b3dde9f25d83035bacf355dee94fcf563abd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9909158",
    "kind": "arxiv",
    "version": 1
  }
}