Pith Number

pith:HRROKOAY

pith:2016:HRROKOAYNSU3RWBB6LXBS2XPKB

not attested not anchored not stored refs pending

Breuil-Kisin Modules via crystalline cohomology

Bryden Cais, Tong Liu

arxiv:1610.09706 v3 · 2016-10-30 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HRROKOAYNSU3RWBB6LXBS2XPKB}

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	2026-05-17T23:50:34.483633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c62e538186ca9b8d821f2ee196aef5054984dc920db5f2df49f7785b72ac2b7

Aliases

arxiv: 1610.09706 · arxiv_version: 1610.09706v3 · doi: 10.48550/arxiv.1610.09706 · pith_short_12: HRROKOAYNSU3 · pith_short_16: HRROKOAYNSU3RWBB · pith_short_8: HRROKOAY

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/HRROKOAYNSU3RWBB6LXBS2XPKB \
  | 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: 3c62e538186ca9b8d821f2ee196aef5054984dc920db5f2df49f7785b72ac2b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acca29a89e619c4c89f41997c3f4856cbda55798edbc6e2ed6a6de29ad5713f6",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-30T20:28:19Z",
    "title_canon_sha256": "4511ad63b1200f3a66ef88aa0c60bedc30ed36c012d74f78ac7558450f35bb3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.09706",
    "kind": "arxiv",
    "version": 3
  }
}