Pith Number

pith:5YTBCNV6

pith:2021:5YTBCNV6QHPAF7AES6BJGCIU75

not attested not anchored not stored refs pending

Relative topos theory via stacks

Olivia Caramello, Riccardo Zanfa

arxiv:2107.04417 v1 · 2021-07-09 · math.AG · 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{5YTBCNV6QHPAF7AES6BJGCIU75}

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

De Morgan's law in toposes I

Receipt and verification

First computed	2026-07-05T02:56:33.134897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee261136be81de02fc049782930914ff779c932e6e0d34906d0cadfdd041cb1a

Aliases

arxiv: 2107.04417 · arxiv_version: 2107.04417v1 · doi: 10.48550/arxiv.2107.04417 · pith_short_12: 5YTBCNV6QHPA · pith_short_16: 5YTBCNV6QHPAF7AE · pith_short_8: 5YTBCNV6

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/5YTBCNV6QHPAF7AES6BJGCIU75 \
  | 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: ee261136be81de02fc049782930914ff779c932e6e0d34906d0cadfdd041cb1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89235d13143e9e0f6df0ddc42a7fe539c4156249d9395a6110f79da4a043830a",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-07-09T13:04:35Z",
    "title_canon_sha256": "09c8224178326a6f4cce7a5ca3c0e9c855dd9cc8ccc20537f2df329f5dd2a227"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.04417",
    "kind": "arxiv",
    "version": 1
  }
}