Pith Number

pith:26KG5MLS

pith:2024:26KG5MLSZYJ5GE3JRIMM7XI6RT

not attested not anchored not stored refs pending

Ramification bounds via Wach modules and q-crystalline cohomology

Pavel \v{C}oupek

arxiv:2410.23453 v2 · 2024-10-30 · 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{26KG5MLSZYJ5GE3JRIMM7XI6RT}

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	2026-05-28T01:04:25.626547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7946eb172ce13d313698a18cfdd1e8ce4127dc75fa50adb7bb51090116cda9c

Aliases

arxiv: 2410.23453 · arxiv_version: 2410.23453v2 · doi: 10.48550/arxiv.2410.23453 · pith_short_12: 26KG5MLSZYJ5 · pith_short_16: 26KG5MLSZYJ5GE3J · pith_short_8: 26KG5MLS

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/26KG5MLSZYJ5GE3JRIMM7XI6RT \
  | 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: d7946eb172ce13d313698a18cfdd1e8ce4127dc75fa50adb7bb51090116cda9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a74ecb14a99592bd6a16183afb7a747b88d5e949d6852db8c2eba685134e2be1",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-10-30T20:51:01Z",
    "title_canon_sha256": "d3ab14de735f6ef548a4bd4a2c9e499fec2c119cb2b969e2a577cb221389cc85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.23453",
    "kind": "arxiv",
    "version": 2
  }
}