Pith Number

pith:XXMFRZSH

pith:2012:XXMFRZSHPB6ZGZ27ZBYCJPMHUE

not attested not anchored not stored refs pending

Exotic smooth structures on topological fibre bundles I

Bruce Williams, Kiyoshi Igusa, Sebastian Goette

arxiv:1203.2203 v3 · 2012-03-09 · math.KT · 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{XXMFRZSHPB6ZGZ27ZBYCJPMHUE}

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	2026-05-18T03:58:24.194296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdd858e647787d93675fc87024bd87a1324f2236540285dc2bfbf8b01a09a6c5

Aliases

arxiv: 1203.2203 · arxiv_version: 1203.2203v3 · doi: 10.48550/arxiv.1203.2203 · pith_short_12: XXMFRZSHPB6Z · pith_short_16: XXMFRZSHPB6ZGZ27 · pith_short_8: XXMFRZSH

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/XXMFRZSHPB6ZGZ27ZBYCJPMHUE \
  | 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: bdd858e647787d93675fc87024bd87a1324f2236540285dc2bfbf8b01a09a6c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ff12cf61731d8afb7648938e86fda1827322e62886915bca620abf961720642",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-03-09T22:48:23Z",
    "title_canon_sha256": "d183cb6bf2b49f9dc4534831fc14f872bd66f7a384cfa707f6a8f04206af01c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2203",
    "kind": "arxiv",
    "version": 3
  }
}