Pith Number

pith:2AEKJFWI

pith:2007:2AEKJFWIIU3NN4YTAINTQLAQS5

not attested not anchored not stored refs pending

Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor

Jeffrey S. Case

arxiv:0712.1321 v2 · 2007-12-09 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2AEKJFWIIU3NN4YTAINTQLAQS5}

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	2026-05-18T04:33:27.452893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d008a496c84536d6f313021b382c109752e3599bd0ea6fde719a23d439a7d522

Aliases

arxiv: 0712.1321 · arxiv_version: 0712.1321v2 · doi: 10.48550/arxiv.0712.1321 · pith_short_12: 2AEKJFWIIU3N · pith_short_16: 2AEKJFWIIU3NN4YT · pith_short_8: 2AEKJFWI

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/2AEKJFWIIU3NN4YTAINTQLAQS5 \
  | 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: d008a496c84536d6f313021b382c109752e3599bd0ea6fde719a23d439a7d522

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0126003c73115137a975d0b85bb8c4af90386b1d61a554ebf70186289b133916",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2007-12-09T20:40:58Z",
    "title_canon_sha256": "980bf29cae3b7e1a1df4a1e587482f6479e1216291f308d77a1abd5166450b59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.1321",
    "kind": "arxiv",
    "version": 2
  }
}