Pith Number

pith:CGOQKAAC

pith:2021:CGOQKAACBF3VQIJZLIKUM76YIZ

not attested not anchored not stored refs pending

General Covariance from the Viewpoint of Stacks

Filip Dul

arxiv:2112.15473 v2 · 2021-12-31 · math-ph · hep-th · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CGOQKAACBF3VQIJZLIKUM76YIZ}

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	2026-07-05T05:43:09.528919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

119d05000209775821395a15467fd84645444f6a79c221ef27d3b6146bddd229

Aliases

arxiv: 2112.15473 · arxiv_version: 2112.15473v2 · doi: 10.48550/arxiv.2112.15473 · pith_short_12: CGOQKAACBF3V · pith_short_16: CGOQKAACBF3VQIJZ · pith_short_8: CGOQKAAC

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/CGOQKAACBF3VQIJZLIKUM76YIZ \
  | 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: 119d05000209775821395a15467fd84645444f6a79c221ef27d3b6146bddd229

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22294e4861bf5d08cdc1289a70c849b388de6f97b5f3ed8a2c0061d3d5f18e2f",
    "cross_cats_sorted": [
      "hep-th",
      "math.DG",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2021-12-31T14:18:22Z",
    "title_canon_sha256": "fae960963a3760a69c6fcbd2506cee93cfe42bffb0f7078a742e0170527b0331"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.15473",
    "kind": "arxiv",
    "version": 2
  }
}