Pith Number

pith:6OQANZUB

pith:2021:6OQANZUB7KTD5DPVLLNWYNWXF7

not attested not anchored not stored refs pending

The minimal model program for arithmetic surfaces enriched by a Brauer class

Colin Ingalls, Daniel Chan

arxiv:2108.03105 v1 · 2021-08-06 · math.AG · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6OQANZUB7KTD5DPVLLNWYNWXF7}

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	2026-07-05T03:03:45.744656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3a006e681faa63e8df55adb6c36d72fc0b6734d1601cf5181d126e784228f20

Aliases

arxiv: 2108.03105 · arxiv_version: 2108.03105v1 · doi: 10.48550/arxiv.2108.03105 · pith_short_12: 6OQANZUB7KTD · pith_short_16: 6OQANZUB7KTD5DPV · pith_short_8: 6OQANZUB

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/6OQANZUB7KTD5DPVLLNWYNWXF7 \
  | 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: f3a006e681faa63e8df55adb6c36d72fc0b6734d1601cf5181d126e784228f20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39cbda28a3b5661156e2b3f0c61758fd21e3191945cb0ad4aad76bd3dd6a15ba",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-08-06T13:12:40Z",
    "title_canon_sha256": "3dd121d59ce6ef5d780d035a808313ab7c878538a9d74ff3b75fbcf999da18a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.03105",
    "kind": "arxiv",
    "version": 1
  }
}