Pith Number

pith:DZ4A3R5U

pith:2025:DZ4A3R5UDCHOBWUMRPUXETH3B3

not attested not anchored not stored refs pending

Morphisms and comorphisms of sites II -- Distributors of sites

Axel Osmond, Olivia Caramello

arxiv:2507.20932 v1 · 2025-07-28 · 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{DZ4A3R5UDCHOBWUMRPUXETH3B3}

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	2026-07-05T11:44:28.396450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e780dc7b4188ee0da8c8be9724cfb0ef83b0b2afb4f276d32d0be2d4a8230c8

Aliases

arxiv: 2507.20932 · arxiv_version: 2507.20932v1 · doi: 10.48550/arxiv.2507.20932 · pith_short_12: DZ4A3R5UDCHO · pith_short_16: DZ4A3R5UDCHOBWUM · pith_short_8: DZ4A3R5U

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/DZ4A3R5UDCHOBWUMRPUXETH3B3 \
  | 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: 1e780dc7b4188ee0da8c8be9724cfb0ef83b0b2afb4f276d32d0be2d4a8230c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfb54804989925a7910821a2a25cba4a286c429eb7233b57d5698b213df7b8ad",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-07-28T15:42:09Z",
    "title_canon_sha256": "4809e9abd3e7ed30daa7a9115737011b65d1f4c03334a937a0a870a1e047fa5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20932",
    "kind": "arxiv",
    "version": 1
  }
}