Pith Number

pith:PQSX222G

pith:2016:PQSX222GX6JZQ65Z7K22KXNDH2

not attested not anchored not stored refs pending

The Poincar\'e-Hopf Theorem for line fields revisited

Diarmuid Crowley, Mark Grant

arxiv:1612.04073 v2 · 2016-12-13 · math.AT · 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{PQSX222GX6JZQ65Z7K22KXNDH2}

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	2026-05-18T00:45:44.146894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c257d6b46bf93987bb9fab5a55da33eab0b9f3be932b00188b902a71de4d343

Aliases

arxiv: 1612.04073 · arxiv_version: 1612.04073v2 · doi: 10.48550/arxiv.1612.04073 · pith_short_12: PQSX222GX6JZ · pith_short_16: PQSX222GX6JZQ65Z · pith_short_8: PQSX222G

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/PQSX222GX6JZQ65Z7K22KXNDH2 \
  | 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: 7c257d6b46bf93987bb9fab5a55da33eab0b9f3be932b00188b902a71de4d343

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b76515d5991af8ddd246da207b77a35137fa327d7c438f878d9a5b51935dd7b0",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-12-13T09:34:57Z",
    "title_canon_sha256": "904c6ede6efa9cadfd8004bcaa5d630dce5e0f509585f05e4610598b984802c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04073",
    "kind": "arxiv",
    "version": 2
  }
}