Pith Number

pith:4RVXJ7OF

pith:2013:4RVXJ7OFX24AXDHEYVC3BDAYNT

not attested not anchored not stored refs pending

Homotopy limits in type theory

Chris Kapulkin, Jeremy Avigad, Peter LeFanu Lumsdaine

arxiv:1304.0680 v3 · 2013-04-02 · math.LO · cs.LO · 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{4RVXJ7OFX24AXDHEYVC3BDAYNT}

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	2026-05-17T23:53:17.728671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e46b74fdc5beb80b8ce4c545b08c186cf7b2b30dcc63c141204d520abcf4ade7

Aliases

arxiv: 1304.0680 · arxiv_version: 1304.0680v3 · doi: 10.48550/arxiv.1304.0680 · pith_short_12: 4RVXJ7OFX24A · pith_short_16: 4RVXJ7OFX24AXDHE · pith_short_8: 4RVXJ7OF

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/4RVXJ7OFX24AXDHEYVC3BDAYNT \
  | 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: e46b74fdc5beb80b8ce4c545b08c186cf7b2b30dcc63c141204d520abcf4ade7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfd4a58ed0025149b83852d5f2671cae3bdb3c4341e58157987cd967422650e4",
    "cross_cats_sorted": [
      "cs.LO",
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-04-02T16:33:50Z",
    "title_canon_sha256": "69a5343169836a0de39e3a481641adc8e218a79950ea75ba21e39a424a95470a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0680",
    "kind": "arxiv",
    "version": 3
  }
}