Pith Number

pith:IMNEK74C

pith:2012:IMNEK74CPTKPPTPXIT36RJ2AMA

not attested not anchored not stored refs pending

Relations in the 24-th homotopy groups of spheres

Juno Mukai, Toshiyuki Miyauchi

arxiv:1207.6170 v1 · 2012-07-26 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IMNEK74CPTKPPTPXIT36RJ2AMA}

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	2026-05-18T03:50:08.667012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

431a457f827cd4f7cdf744f7e8a7406026b8a74baec040ca7326cfeec18f45cf

Aliases

arxiv: 1207.6170 · arxiv_version: 1207.6170v1 · doi: 10.48550/arxiv.1207.6170 · pith_short_12: IMNEK74CPTKP · pith_short_16: IMNEK74CPTKPPTPX · pith_short_8: IMNEK74C

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/IMNEK74CPTKPPTPXIT36RJ2AMA \
  | 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: 431a457f827cd4f7cdf744f7e8a7406026b8a74baec040ca7326cfeec18f45cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "790bfdcabe4b6bb3adbb4351eea7862e400822cb17714d9595857dd12af6180a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-07-26T05:16:12Z",
    "title_canon_sha256": "c63d523b5ac3875cfa854d7c86bc3de53b3999dd4899c17e0cfd4f187ab457e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6170",
    "kind": "arxiv",
    "version": 1
  }
}