Pith Number

pith:PVW4FT4H

pith:2012:PVW4FT4H2IBAX3WLSEVAXODPCJ

not attested not anchored not stored refs pending

Low Degree Places on the Modular Curve X1(N)

Mark van Hoeij

arxiv:1202.4355 v5 · 2012-02-20 · 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{PVW4FT4H2IBAX3WLSEVAXODPCJ}

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	2026-05-18T02:49:18.708527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d6dc2cf87d2020beecb912a0bb86f127f39a68171fdc4b2d41c786bb0726093

Aliases

arxiv: 1202.4355 · arxiv_version: 1202.4355v5 · doi: 10.48550/arxiv.1202.4355 · pith_short_12: PVW4FT4H2IBA · pith_short_16: PVW4FT4H2IBAX3WL · pith_short_8: PVW4FT4H

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/PVW4FT4H2IBAX3WLSEVAXODPCJ \
  | 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: 7d6dc2cf87d2020beecb912a0bb86f127f39a68171fdc4b2d41c786bb0726093

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb84f147a1552a9cd1d0310f26632fc26a4c46c470193c3bca68226cb817af5f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-02-20T15:23:20Z",
    "title_canon_sha256": "b0b768e7daedb30a56527a83a15f52d3f8e8aebb7743bd35da6934dea73d1d27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.4355",
    "kind": "arxiv",
    "version": 5
  }
}