Pith Number

pith:O2ESNX37

pith:2017:O2ESNX37URIHJZKSW4UI326WCW

not attested not anchored not stored refs pending

Linear Equations in Singular Moduli

Lars K\"uhne, Yuri Bilu

arxiv:1712.04027 v1 · 2017-12-11 · 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{O2ESNX37URIHJZKSW4UI326WCW}

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	2026-05-18T00:28:09.517950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

768926df7fa45074e552b7288debd615983160719c562f09ed5ae2c4f4a3728a

Aliases

arxiv: 1712.04027 · arxiv_version: 1712.04027v1 · doi: 10.48550/arxiv.1712.04027 · pith_short_12: O2ESNX37URIH · pith_short_16: O2ESNX37URIHJZKS · pith_short_8: O2ESNX37

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/O2ESNX37URIHJZKSW4UI326WCW \
  | 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: 768926df7fa45074e552b7288debd615983160719c562f09ed5ae2c4f4a3728a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee9734f3353e58beea764143141d99e43880431278a7149d0ef0d21ae7395c2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-12-11T21:08:26Z",
    "title_canon_sha256": "745d2f353fafd956a5e372c105672f469c439e30c7f7c0c74fb9ef0064f64dd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.04027",
    "kind": "arxiv",
    "version": 1
  }
}