Pith Number

pith:YTINBXJE

pith:2011:YTINBXJEGXE3AVFIIUMH456CLB

not attested not anchored not stored refs pending

A combinatorial description of homotopy groups of spheres

Jie Wu, Roman Mikhailov

arxiv:1108.3055 v1 · 2011-08-15 · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YTINBXJEGXE3AVFIIUMH456CLB}

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	2026-05-18T04:15:28.746850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4d0d0dd2435c9b054a845187e77c258603b49a9a1db825cf00959bd661eed6c

Aliases

arxiv: 1108.3055 · arxiv_version: 1108.3055v1 · doi: 10.48550/arxiv.1108.3055 · pith_short_12: YTINBXJEGXE3 · pith_short_16: YTINBXJEGXE3AVFI · pith_short_8: YTINBXJE

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/YTINBXJEGXE3AVFIIUMH456CLB \
  | 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: c4d0d0dd2435c9b054a845187e77c258603b49a9a1db825cf00959bd661eed6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a63808a3a6b575026ad0908f494ece5ba931f456eef77d4a77a82c7b6bd5df44",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-08-15T18:50:24Z",
    "title_canon_sha256": "c5b5072d05dceb1cad4feb97a8954a3a5409664d0d8e8101761b9588f607c6ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3055",
    "kind": "arxiv",
    "version": 1
  }
}