Pith Number

pith:D2YSRM4P

pith:2011:D2YSRM4PNR5MJ5YVM63T6WKK2D

not attested not anchored not stored refs pending

The cobordism category and Waldhausen's K-theory

Ib Madsen, M. B\"okstedt

arxiv:1102.4155 v1 · 2011-02-21 · math.AT · 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{D2YSRM4PNR5MJ5YVM63T6WKK2D}

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	2026-05-18T04:27:35.481392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1eb128b38f6c7ac4f71567b73f594ad0fdce0f737b60f002f159c6bbb9d03330

Aliases

arxiv: 1102.4155 · arxiv_version: 1102.4155v1 · doi: 10.48550/arxiv.1102.4155 · pith_short_12: D2YSRM4PNR5M · pith_short_16: D2YSRM4PNR5MJ5YV · pith_short_8: D2YSRM4P

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/D2YSRM4PNR5MJ5YVM63T6WKK2D \
  | 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: 1eb128b38f6c7ac4f71567b73f594ad0fdce0f737b60f002f159c6bbb9d03330

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ade5366d7a66e82667c1ffb391fd330b04d0353595c06fce4498409286740c5b",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-02-21T08:14:06Z",
    "title_canon_sha256": "314ac2a1194fa9c32974105e1b6085a90613a5fb1e10a0248362fe8387bc1d92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4155",
    "kind": "arxiv",
    "version": 1
  }
}