Pith Number

pith:6YAP7AKR

pith:2012:6YAP7AKRQYCGQ2443GDZPYANJE

not attested not anchored not stored refs pending

The 2-components of the 31-stem homotopy groups of the 9 and 10-spheres

Juno Mukai, Tomohisa Inoue

arxiv:1210.0995 v1 · 2012-10-03 · 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{6YAP7AKRQYCGQ2443GDZPYANJE}

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	2026-05-18T03:44:13.137218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f600ff81518604686b9cd98797e00d49321e1d10d82393d91be428e41c0109b5

Aliases

arxiv: 1210.0995 · arxiv_version: 1210.0995v1 · doi: 10.48550/arxiv.1210.0995 · pith_short_12: 6YAP7AKRQYCG · pith_short_16: 6YAP7AKRQYCGQ244 · pith_short_8: 6YAP7AKR

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/6YAP7AKRQYCGQ2443GDZPYANJE \
  | 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: f600ff81518604686b9cd98797e00d49321e1d10d82393d91be428e41c0109b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60cbf855b2ed3f5ef992efb67d3cdba06c65c770ad9b1bee3f8167e9a7d871f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-10-03T06:13:24Z",
    "title_canon_sha256": "647947792f65520c4318a1273adacfe579efa9a344a413549eb893bd85a1d180"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0995",
    "kind": "arxiv",
    "version": 1
  }
}