Pith Number

pith:Y3P6KR6D

pith:2015:Y3P6KR6DEYKTILU2RLSZ5B36HJ

not attested not anchored not stored refs pending

Kan extensions and the calculus of modules for $\infty$-categories

Dominic Verity, Emily Riehl

arxiv:1507.01460 v3 · 2015-07-06 · math.CT · 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{Y3P6KR6DEYKTILU2RLSZ5B36HJ}

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	2026-05-18T00:51:18.512198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6dfe547c32615342e9a8ae59e877e3a42cc069882a3fc073bcf9eaa9f60a26c

Aliases

arxiv: 1507.01460 · arxiv_version: 1507.01460v3 · doi: 10.48550/arxiv.1507.01460 · pith_short_12: Y3P6KR6DEYKT · pith_short_16: Y3P6KR6DEYKTILU2 · pith_short_8: Y3P6KR6D

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/Y3P6KR6DEYKTILU2RLSZ5B36HJ \
  | 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: c6dfe547c32615342e9a8ae59e877e3a42cc069882a3fc073bcf9eaa9f60a26c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "036aa35d50b8c1644fb3c76590495f5ec891be897d6fd32512fbba7d08aee490",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-07-06T13:47:37Z",
    "title_canon_sha256": "69dbeb6284328ad0f10ddc2a3a8a58db09d54a97551d9592f8499d4918cd805c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01460",
    "kind": "arxiv",
    "version": 3
  }
}