Pith Number

pith:AWLJ6MVS

pith:2019:AWLJ6MVSF63BNK2MZLBE24J4T4

not attested not anchored not stored refs pending

Degeneracy Index and Poincar\'e-Hopf Theorem

Haibo Ruan, Jorge Zanelli

arxiv:1907.01473 v2 · 2019-07-02 · math-ph · hep-th · math.DS · 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{AWLJ6MVSF63BNK2MZLBE24J4T4}

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	2026-07-05T03:27:24.012602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05969f32b22fb616ab4ccac24d713c9f2af6c7047a5b60abcb5bb5a799b6e567

Aliases

arxiv: 1907.01473 · arxiv_version: 1907.01473v2 · doi: 10.48550/arxiv.1907.01473 · pith_short_12: AWLJ6MVSF63B · pith_short_16: AWLJ6MVSF63BNK2M · pith_short_8: AWLJ6MVS

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/AWLJ6MVSF63BNK2MZLBE24J4T4 \
  | 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: 05969f32b22fb616ab4ccac24d713c9f2af6c7047a5b60abcb5bb5a799b6e567

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96b7908b40c48fece810378deb9bfef2d44ee97abc41705cf3a666a52e5c1133",
    "cross_cats_sorted": [
      "hep-th",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-07-02T16:08:23Z",
    "title_canon_sha256": "de2f4be5699fdae841b0130c222ab4eb84201747320755567ef1b5577d0aa7a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.01473",
    "kind": "arxiv",
    "version": 2
  }
}