Pith Number

pith:YZLKCA3G

pith:2011:YZLKCA3GUL7YR3GPCTPG3IMB5W

not attested not anchored not stored refs pending

Local-global principles for torsors over arithmetic curves

Daniel Krashen, David Harbater, Julia Hartmann

arxiv:1108.3323 v5 · 2011-08-16 · math.NT · math.AG · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZLKCA3GUL7YR3GPCTPG3IMB5W}

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	2026-05-18T02:29:55.445567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c656a10366a2ff88eccf14de6da181edbdfd26b3b5b0da5fdac7ea8961e95128

Aliases

arxiv: 1108.3323 · arxiv_version: 1108.3323v5 · doi: 10.48550/arxiv.1108.3323 · pith_short_12: YZLKCA3GUL7Y · pith_short_16: YZLKCA3GUL7YR3GP · pith_short_8: YZLKCA3G

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/YZLKCA3GUL7YR3GPCTPG3IMB5W \
  | 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: c656a10366a2ff88eccf14de6da181edbdfd26b3b5b0da5fdac7ea8961e95128

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf243fa11500d1595de80421871d508decf25018803a4e15f9a4a993e5248abd",
    "cross_cats_sorted": [
      "math.AG",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-16T19:22:19Z",
    "title_canon_sha256": "1b631fd2f81bae31315f679c107a6ce682072e21fd92f7fe5b6940aea5ed3714"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3323",
    "kind": "arxiv",
    "version": 5
  }
}