Pith Number

pith:D5BIV4AT

pith:2010:D5BIV4ATGHWFE4RVT3LVNBUSQL

not attested not anchored not stored refs pending

On arithmetic families of filtered phi-modules and crystalline representations

Eugen Hellmann

arxiv:1010.4577 v2 · 2010-10-21 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D5BIV4ATGHWFE4RVT3LVNBUSQL}

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	2026-05-18T02:23:38.823461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f428af01331ec5272359ed756869282c5a824a0884885c2feb15ad8034cdf3b

Aliases

arxiv: 1010.4577 · arxiv_version: 1010.4577v2 · doi: 10.48550/arxiv.1010.4577 · pith_short_12: D5BIV4ATGHWF · pith_short_16: D5BIV4ATGHWFE4RV · pith_short_8: D5BIV4AT

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/D5BIV4ATGHWFE4RVT3LVNBUSQL \
  | 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: 1f428af01331ec5272359ed756869282c5a824a0884885c2feb15ad8034cdf3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ca5bf27ee1958ef8f76a26453b18f619f1e428c8a2d85be0df2a3fb41f5e175",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-10-21T20:25:58Z",
    "title_canon_sha256": "e563010a234853df73d97ce1010220b3ba901d25f38dcb06d4feb5544885fffe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4577",
    "kind": "arxiv",
    "version": 2
  }
}