Pith Number

pith:5F7AQRIS

pith:2015:5F7AQRIS4YFAZ2BRZZ4GERK3W5

not attested not anchored not stored refs pending

Asymptotic properties of MMM-classes

Jonathan Bowden

arxiv:1509.02362 v1 · 2015-09-08 · math.AT · math.GR · 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{5F7AQRIS4YFAZ2BRZZ4GERK3W5}

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	2026-05-18T01:33:41.076515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e97e084512e60a0ce831ce7862455bb76c8d79cc1e21854325515423095ecd44

Aliases

arxiv: 1509.02362 · arxiv_version: 1509.02362v1 · doi: 10.48550/arxiv.1509.02362 · pith_short_12: 5F7AQRIS4YFA · pith_short_16: 5F7AQRIS4YFAZ2BR · pith_short_8: 5F7AQRIS

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/5F7AQRIS4YFAZ2BRZZ4GERK3W5 \
  | 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: e97e084512e60a0ce831ce7862455bb76c8d79cc1e21854325515423095ecd44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "989e9cf7c81eecb2f38930a14dff60398e54b190c231b8bb80c09ee25beebe41",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-09-08T13:22:03Z",
    "title_canon_sha256": "be823554b6bd1fb06e6afba98c0cd4af43e626e1509dd2166ca83897cc3db8ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02362",
    "kind": "arxiv",
    "version": 1
  }
}