Pith Number

pith:4FP6FVE7

pith:2012:4FP6FVE7GLMUOZFENXOX4GZ4MM

not attested not anchored not stored refs pending

Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

James D.E. Grant, Jan-Hendrik Treude

arxiv:1201.4249 v1 · 2012-01-20 · gr-qc · math-ph · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4FP6FVE7GLMUOZFENXOX4GZ4MM}

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	2026-05-18T03:30:42.314641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e15fe2d49f32d94764a46ddd7e1b3c632971907a3358abc1f7fc42ee4ca8f66e

Aliases

arxiv: 1201.4249 · arxiv_version: 1201.4249v1 · doi: 10.48550/arxiv.1201.4249 · pith_short_12: 4FP6FVE7GLMU · pith_short_16: 4FP6FVE7GLMUOZFE · pith_short_8: 4FP6FVE7

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/4FP6FVE7GLMUOZFENXOX4GZ4MM \
  | 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: e15fe2d49f32d94764a46ddd7e1b3c632971907a3358abc1f7fc42ee4ca8f66e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74986f0d4b1503846bcc96c0e75f8419eb2e318a2147c1f4d0bfaa44f6fe03a9",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-01-20T10:22:14Z",
    "title_canon_sha256": "85933dc92eae3f0d198b62d2f2e3693396e33f002de836eff82af6973e5c09b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4249",
    "kind": "arxiv",
    "version": 1
  }
}