Pith Number

pith:KFK4DZS5

pith:2010:KFK4DZS5U3HZAQCDAWW6QLA3Y6

not attested not anchored not stored refs pending

In the category of relative categories the Rezk equivalences are exactly the DK-equivalences

C. Barwick, D. M. Kan

arxiv:1012.1541 v2 · 2010-12-07 · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KFK4DZS5U3HZAQCDAWW6QLA3Y6}

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	2026-05-18T04:32:02.441541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5155c1e65da6cf90404305ade82c1bc7acfbe64a4d9920389160982b06c42f23

Aliases

arxiv: 1012.1541 · arxiv_version: 1012.1541v2 · doi: 10.48550/arxiv.1012.1541 · pith_short_12: KFK4DZS5U3HZ · pith_short_16: KFK4DZS5U3HZAQCD · pith_short_8: KFK4DZS5

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/KFK4DZS5U3HZAQCDAWW6QLA3Y6 \
  | 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: 5155c1e65da6cf90404305ade82c1bc7acfbe64a4d9920389160982b06c42f23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0261aab69075650c53480d10896c4dda91db000660a952d1939a4c08815bc1f",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-12-07T16:00:25Z",
    "title_canon_sha256": "c93a387a68d82b5ad9ca4ad37c0c39a971f819baf06bd8b688c4dd699f1b96ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1541",
    "kind": "arxiv",
    "version": 2
  }
}