Pith Number

pith:QLJQNW4B

pith:2008:QLJQNW4B4SCNMDYCRI2AG4SOKC

not attested not anchored not stored refs pending

Linear series on semistable curves

Lucia Caporaso

arxiv:0812.1682 v4 · 2008-12-09 · 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{QLJQNW4B4SCNMDYCRI2AG4SOKC}

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	2026-05-18T04:39:18.461018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82d306db81e484d60f028a3403724e50b71cd902b7f42a77bb7c4ce7f7742859

Aliases

arxiv: 0812.1682 · arxiv_version: 0812.1682v4 · doi: 10.48550/arxiv.0812.1682 · pith_short_12: QLJQNW4B4SCN · pith_short_16: QLJQNW4B4SCNMDYC · pith_short_8: QLJQNW4B

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/QLJQNW4B4SCNMDYCRI2AG4SOKC \
  | 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: 82d306db81e484d60f028a3403724e50b71cd902b7f42a77bb7c4ce7f7742859

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c84c7365af5bac35e2de02ceb2b911fd0a8f95979409126d516535db7b7b1f33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2008-12-09T12:52:48Z",
    "title_canon_sha256": "d63e3177a326ba46c20fdce9d7bc106d7da8a0200f54626cc88cd190e580fc06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1682",
    "kind": "arxiv",
    "version": 4
  }
}