Pith Number

pith:5TNAM7CN

pith:2025:5TNAM7CNPLK4CQUCJOHO2DM2H5

not attested not anchored not stored refs pending

Local fibrations and morphisms of relative toposes

L\'eo Bartoli, Olivia Caramello

arxiv:2507.14379 v1 · 2025-07-18 · 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{5TNAM7CNPLK4CQUCJOHO2DM2H5}

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	2026-07-05T11:40:05.150692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecda067c4d7ad5c142824b8eed0d9a3f591cd3c37fe57fe14a391a30ddf95014

Aliases

arxiv: 2507.14379 · arxiv_version: 2507.14379v1 · doi: 10.48550/arxiv.2507.14379 · pith_short_12: 5TNAM7CNPLK4 · pith_short_16: 5TNAM7CNPLK4CQUC · pith_short_8: 5TNAM7CN

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/5TNAM7CNPLK4CQUCJOHO2DM2H5 \
  | 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: ecda067c4d7ad5c142824b8eed0d9a3f591cd3c37fe57fe14a391a30ddf95014

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12a8cc8b2618d5ca8157e3d67b8cbd1973d1150bee43714a84042b79af620bf9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-07-18T21:58:10Z",
    "title_canon_sha256": "28e6b7fa44832946f6c4abb38ba75e9335d0d43188ff38885d90574ba41c5e35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.14379",
    "kind": "arxiv",
    "version": 1
  }
}