Pith Number

pith:242AIO26

pith:2026:242AIO265L5XOZSHWRKFW2K6AH

not attested not anchored not stored refs pending

Tropical and algebraic elliptic plane curves with fixed j-invariant

Alessio Cela, Sae Koyama

arxiv:2608.13081 v1 · 2026-08-13 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{242AIO265L5XOZSHWRKFW2K6AH}

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	2026-08-14T01:00:17.599796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d734043b5eeafb776647b4545b695e01c58a993d89349fa7805626978b146668

Aliases

arxiv: 2608.13081 · arxiv_version: 2608.13081v1 · doi: 10.48550/arxiv.2608.13081 · pith_short_12: 242AIO265L5X · pith_short_16: 242AIO265L5XOZSH · pith_short_8: 242AIO26

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/242AIO265L5XOZSHWRKFW2K6AH \
  | 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: d734043b5eeafb776647b4545b695e01c58a993d89349fa7805626978b146668

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd39ad34f2c521c9284afa633c7d779c63fdcccfd143b1b4495c9be93063ffc4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-08-13T10:52:20Z",
    "title_canon_sha256": "e167ef4861f25157504e6b650aafdcb095191731345ba11d75acf964b11fbc20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.13081",
    "kind": "arxiv",
    "version": 1
  }
}