Pith Number

pith:PDKYGKWE

pith:2011:PDKYGKWEPM6BE46BIIBH2D7SFA

not attested not anchored not stored refs pending

Pontryagin invariants and integral formulas for Milnor's triple linking number

Clayton Shonkwiler, David Shea Vela-Vick, Dennis DeTurck, Herman Gluck, Paul Melvin, Rafal Komendarczyk

arxiv:1101.3374 v1 · 2011-01-18 · math.GT · math-ph · math.AT · math.DG · math.MP · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PDKYGKWEPM6BE46BIIBH2D7SFA}

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	2026-05-18T00:57:32.268890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78d5832ac47b3c1273c142027d0ff2283c69f38c926aea735d0022a2d2e8edc8

Aliases

arxiv: 1101.3374 · arxiv_version: 1101.3374v1 · doi: 10.48550/arxiv.1101.3374 · pith_short_12: PDKYGKWEPM6B · pith_short_16: PDKYGKWEPM6BE46B · pith_short_8: PDKYGKWE

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/PDKYGKWEPM6BE46BIIBH2D7SFA \
  | 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: 78d5832ac47b3c1273c142027d0ff2283c69f38c926aea735d0022a2d2e8edc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45f1c49f416f56dcdccc9bb01adacf6b6604ceb5c42b867e03d27120093bc21e",
    "cross_cats_sorted": [
      "math-ph",
      "math.AT",
      "math.DG",
      "math.MP",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-01-18T03:06:00Z",
    "title_canon_sha256": "0fa14e8804a0d4832c3c73835fafc2fd9691aaa7a816cd4b5d7451ba20634b7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3374",
    "kind": "arxiv",
    "version": 1
  }
}