Pith Number

pith:I3RTDWU5

pith:2015:I3RTDWU5HU3Q3EUT5Q2Q2ZHWOY

not attested not anchored not stored refs pending

Elliptic curves over $\mathbb{Q}_\infty$ are modular

Jack A. Thorne

arxiv:1505.04769 v1 · 2015-05-18 · 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{I3RTDWU5HU3Q3EUT5Q2Q2ZHWOY}

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	2026-05-18T02:07:24.641870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46e331da9d3d370d9293ec350d64f6762915564a64ece2e7226f9dc8bc9c1d2c

Aliases

arxiv: 1505.04769 · arxiv_version: 1505.04769v1 · doi: 10.48550/arxiv.1505.04769 · pith_short_12: I3RTDWU5HU3Q · pith_short_16: I3RTDWU5HU3Q3EUT · pith_short_8: I3RTDWU5

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/I3RTDWU5HU3Q3EUT5Q2Q2ZHWOY \
  | 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: 46e331da9d3d370d9293ec350d64f6762915564a64ece2e7226f9dc8bc9c1d2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "191d953edd25636e038689c294dd99f9b323cd8653a5f257b4a33da32e0cacc2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-05-18T19:30:16Z",
    "title_canon_sha256": "f2f84491381c8799b6d27669f77df8e51f1f6fc06fcdd051fc5fb8f3b7b7fee1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04769",
    "kind": "arxiv",
    "version": 1
  }
}