Pith Number

pith:XIDOBY6W

pith:2025:XIDOBY6WMFKJCM55SIV65X2MOV

not attested not anchored not stored refs pending

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$

Kenji Terao

arxiv:2507.13199 v1 · 2025-07-17 · 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{XIDOBY6WMFKJCM55SIV65X2MOV}

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	2026-07-05T11:38:56.229698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba06e0e3d661549133bd922beedf4c756aa7724a51a2c3cde052d3a4ae8f2a06

Aliases

arxiv: 2507.13199 · arxiv_version: 2507.13199v1 · doi: 10.48550/arxiv.2507.13199 · pith_short_12: XIDOBY6WMFKJ · pith_short_16: XIDOBY6WMFKJCM55 · pith_short_8: XIDOBY6W

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/XIDOBY6WMFKJCM55SIV65X2MOV \
  | 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: ba06e0e3d661549133bd922beedf4c756aa7724a51a2c3cde052d3a4ae8f2a06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b0634bf8841396996c8b70cd4d84b5d17ac9e53c902a9fa75e1062f56088943",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-17T15:09:53Z",
    "title_canon_sha256": "caf48f28ee6803346c424b79f4a6993bc1484a25df4804d9def692066d92dc26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13199",
    "kind": "arxiv",
    "version": 1
  }
}