Pith Number

pith:UVFHQRK2

pith:2019:UVFHQRK2ANKYSN2LVSUB6TK3AL

not attested not anchored not stored refs pending

Poincare Hopf for vector fields on graphs

Oliver Knill

arxiv:1911.04208 v1 · 2019-11-11 · math.CO · cs.DM · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UVFHQRK2ANKYSN2LVSUB6TK3AL}

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

Dehn Sommerville Manifolds

Receipt and verification

First computed	2026-07-05T00:18:18.940888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a54a78455a035589374baca81f4d5b02edc3dffafd79c7404482b21f4e67fc1e

Aliases

arxiv: 1911.04208 · arxiv_version: 1911.04208v1 · doi: 10.48550/arxiv.1911.04208 · pith_short_12: UVFHQRK2ANKY · pith_short_16: UVFHQRK2ANKYSN2L · pith_short_8: UVFHQRK2

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/UVFHQRK2ANKYSN2LVSUB6TK3AL \
  | 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: a54a78455a035589374baca81f4d5b02edc3dffafd79c7404482b21f4e67fc1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1925da648d669430e9dd70b7e651d4179cc048a88ce38d57a0d3a65e4b05261",
    "cross_cats_sorted": [
      "cs.DM",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-11-11T12:20:10Z",
    "title_canon_sha256": "ac4efb39b2db118da2f0bffba9ac3d9759c950743b97c2f85c8f88f46cdfc886"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.04208",
    "kind": "arxiv",
    "version": 1
  }
}