Pith Number

pith:QULLD7PH

pith:2013:QULLD7PHVT7CZDRJATT6EPC4TY

not attested not anchored not stored refs pending

Computing Puiseux Expansions at Cusps of the Modular Curve X0(N)

Mark van Hoeij

arxiv:1307.1627 v1 · 2013-07-05 · math.NT · cs.SC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QULLD7PHVT7CZDRJATT6EPC4TY}

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	2026-05-18T03:19:12.363176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8516b1fde7acfe2c8e2904e7e23c5c9e00da9ac535d95614d244e45f96aa6e20

Aliases

arxiv: 1307.1627 · arxiv_version: 1307.1627v1 · doi: 10.48550/arxiv.1307.1627 · pith_short_12: QULLD7PHVT7C · pith_short_16: QULLD7PHVT7CZDRJ · pith_short_8: QULLD7PH

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/QULLD7PHVT7CZDRJATT6EPC4TY \
  | 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: 8516b1fde7acfe2c8e2904e7e23c5c9e00da9ac535d95614d244e45f96aa6e20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea7af117308e39cf732ef33fea997ac674aebd15e3cb51caf0c84dfa23a7c3c1",
    "cross_cats_sorted": [
      "cs.SC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-07-05T14:57:13Z",
    "title_canon_sha256": "2f70bfd847d1f0c9ee5d4a1b936540db9c2a31314aae60638ce97dadde90a69b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1627",
    "kind": "arxiv",
    "version": 1
  }
}