Pith Number

pith:5Z3MIZLK

pith:2025:5Z3MIZLKZVF4C6ZTWO2BXEODEZ

not attested not anchored not stored refs pending

Pullbacks in tangent categories and tangent display maps

Geoffrey Cruttwell, Marcello Lanfranchi

arxiv:2502.20699 v1 · 2025-02-28 · math.CT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5Z3MIZLKZVF4C6ZTWO2BXEODEZ}

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.

Cited by

1 paper in Pith

Ehresmann connections in tangent categories

Receipt and verification

First computed	2026-07-05T10:21:38.160489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee76c4656acd4bc17b33b3b41b91c326453a54ee772d975d9dac3e6a3acd59a1

Aliases

arxiv: 2502.20699 · arxiv_version: 2502.20699v1 · doi: 10.48550/arxiv.2502.20699 · pith_short_12: 5Z3MIZLKZVF4 · pith_short_16: 5Z3MIZLKZVF4C6ZT · pith_short_8: 5Z3MIZLK

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/5Z3MIZLKZVF4C6ZTWO2BXEODEZ \
  | 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: ee76c4656acd4bc17b33b3b41b91c326453a54ee772d975d9dac3e6a3acd59a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab05a84e28b748f17980a9083f87b1356997b094e6fff3eb2cbdb061860c8a17",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-02-28T04:17:31Z",
    "title_canon_sha256": "c3269e78f53ea12baf2ff27b82195c7efd68cbcfd14b0eef329d9375b8754ba5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.20699",
    "kind": "arxiv",
    "version": 1
  }
}