Pith Number

pith:W4WIPYIR

pith:2013:W4WIPYIRLPKQ2XQZIUVMVF64Z2

not attested not anchored not stored refs pending

Cluster categories for topologists

Julia E. Bergner, Marcy Robertson

arxiv:1308.2560 v3 · 2013-08-12 · math.AT · math.CT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4WIPYIRLPKQ2XQZIUVMVF64Z2}

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	2026-05-18T02:37:44.800224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b72c87e1115bd50d5e19452aca97dcce84dc69b8a0d152e33dd16a810510aca7

Aliases

arxiv: 1308.2560 · arxiv_version: 1308.2560v3 · doi: 10.48550/arxiv.1308.2560 · pith_short_12: W4WIPYIRLPKQ · pith_short_16: W4WIPYIRLPKQ2XQZ · pith_short_8: W4WIPYIR

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/W4WIPYIRLPKQ2XQZIUVMVF64Z2 \
  | 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: b72c87e1115bd50d5e19452aca97dcce84dc69b8a0d152e33dd16a810510aca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74b73b9aaecdc4b2314d3ebf64c0f5ab00a9f0a1dc333ca17320229c8d18a11a",
    "cross_cats_sorted": [
      "math.CT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2013-08-12T13:52:47Z",
    "title_canon_sha256": "3c007b0f3efcba061fbab55dbf08dadd3358dee2d81a59464ec73515685ccc93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2560",
    "kind": "arxiv",
    "version": 3
  }
}