Pith Number

pith:EZUCJL43

pith:2004:EZUCJL432G4DHS423QS2ZTW3FF

not attested not anchored not stored refs pending

Nontrivial classes in $H^*(Imb(S^1,\R^n))$ from nontrivalent graph cocycles

Riccardo Longoni

arxiv:math/0404196 v2 · 2004-04-09 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EZUCJL432G4DHS423QS2ZTW3FF}

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	2026-05-18T01:38:28.421550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

266824af9bd1b833cb9adc25accedb2949fe44c52c425f16523b17b6e534ce0f

Aliases

arxiv: math/0404196 · arxiv_version: math/0404196v2 · doi: 10.48550/arxiv.math/0404196 · pith_short_12: EZUCJL432G4D · pith_short_16: EZUCJL432G4DHS42 · pith_short_8: EZUCJL43

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/EZUCJL432G4DHS423QS2ZTW3FF \
  | 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: 266824af9bd1b833cb9adc25accedb2949fe44c52c425f16523b17b6e534ce0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8059f841efe0f0a77631ea262ef301beab1c3110da92a45d6aaa0a4abc3770ac",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-04-09T11:24:32Z",
    "title_canon_sha256": "afe3fefe730f7a3abe66a41a2a1b98fd3fb60968fdb92e2628756d879f86dd32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404196",
    "kind": "arxiv",
    "version": 2
  }
}