Pith Number

pith:CKBD5HGF

pith:2025:CKBD5HGF7K52QZLAV3DJNUFW6O

not attested not anchored not stored refs pending

Generalised ultracategories and conceptual completeness of geometric logic

Ali Hamad

arxiv:2507.07922 v3 · 2025-07-10 · math.CT · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CKBD5HGF7K52QZLAV3DJNUFW6O}

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

Duality theory for categorical theories

Receipt and verification

First computed	2026-06-09T02:08:31.629417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12823e9cc5fabba86560aec696d0b6f3bbe341bc153b9c39a23abaa6c3f391cc

Aliases

arxiv: 2507.07922 · arxiv_version: 2507.07922v3 · doi: 10.48550/arxiv.2507.07922 · pith_short_12: CKBD5HGF7K52 · pith_short_16: CKBD5HGF7K52QZLA · pith_short_8: CKBD5HGF

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/CKBD5HGF7K52QZLAV3DJNUFW6O \
  | 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: 12823e9cc5fabba86560aec696d0b6f3bbe341bc153b9c39a23abaa6c3f391cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40ced1fc4225aec5f66eb7129c1ab2d266a7d1b78e7bec14eefd6f5ad363025c",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-07-10T17:03:04Z",
    "title_canon_sha256": "ed93e325ccd4e7bd7d993322914193aa168ee213425d6029af956dec6ee512af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.07922",
    "kind": "arxiv",
    "version": 3
  }
}