Pith Number

pith:BFDQPTTG

pith:2011:BFDQPTTGTDTGTPU6EFMOD7ZTGG

not attested not anchored not stored refs pending

Crystalline extensions and the weight part of Serre's conjecture

David Savitt, Toby Gee, Tong Liu

arxiv:1106.5584 v1 · 2011-06-28 · 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{BFDQPTTGTDTGTPU6EFMOD7ZTGG}

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	2026-05-18T04:19:12.893654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

094707ce6698e669be9e2158e1ff333190ef02cb951d03ac2925caa69796380c

Aliases

arxiv: 1106.5584 · arxiv_version: 1106.5584v1 · doi: 10.48550/arxiv.1106.5584 · pith_short_12: BFDQPTTGTDTG · pith_short_16: BFDQPTTGTDTGTPU6 · pith_short_8: BFDQPTTG

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/BFDQPTTGTDTGTPU6EFMOD7ZTGG \
  | 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: 094707ce6698e669be9e2158e1ff333190ef02cb951d03ac2925caa69796380c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd50b513f23d40212cf96b55dddce768a8312d7724797a28831a574bd1ec33b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-06-28T08:05:39Z",
    "title_canon_sha256": "5df7c134b1aa7ba94e63ee0bdb8536c174d4e0913b0ef7c2febfca6bc0298e3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5584",
    "kind": "arxiv",
    "version": 1
  }
}