Pith Number

pith:WV7JYKMD

pith:2020:WV7JYKMDOWQL3VJOMK6O7IFBVH

not attested not anchored not stored refs pending

Hodge-Witt decomposition of relative crystalline cohomology

Andreas Langer, Oliver Gregory

arxiv:2006.13550 v3 · 2020-06-24 · 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{WV7JYKMDOWQL3VJOMK6O7IFBVH}

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	2026-07-05T03:03:37.926393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b57e9c298375a0bdd52e62bcefa0a1a9d633a18fdd24c79493f4e31e23c7bb2a

Aliases

arxiv: 2006.13550 · arxiv_version: 2006.13550v3 · doi: 10.48550/arxiv.2006.13550 · pith_short_12: WV7JYKMDOWQL · pith_short_16: WV7JYKMDOWQL3VJO · pith_short_8: WV7JYKMD

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/WV7JYKMDOWQL3VJOMK6O7IFBVH \
  | 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: b57e9c298375a0bdd52e62bcefa0a1a9d633a18fdd24c79493f4e31e23c7bb2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcab8633b7141d18779f81de7191f4d5664061b91a04aabd8c13edda1e89ea4d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2020-06-24T08:16:57Z",
    "title_canon_sha256": "290efa6921427b8bf3b280624e4909af1b4fbeabe8d1b5306e98c8756b4d610a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.13550",
    "kind": "arxiv",
    "version": 3
  }
}