Pith Number

pith:LPFCGR5B

pith:2026:LPFCGR5BY5CT4PHZCTYDY3BIOL

not attested not anchored not stored refs pending

Minimal genus trisection diagrams of the elliptic surfaces $E(n)$ via handle diagrams

Tsukasa Isoshima

arxiv:2606.02159 v1 · 2026-06-01 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPFCGR5BY5CT4PHZCTYDY3BIOL}

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	2026-06-02T02:05:08.093216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bca2347a1c7453e3cf914f03c6c2872f4ddd07072897900c7f977071061e244

Aliases

arxiv: 2606.02159 · arxiv_version: 2606.02159v1 · doi: 10.48550/arxiv.2606.02159 · pith_short_12: LPFCGR5BY5CT · pith_short_16: LPFCGR5BY5CT4PHZ · pith_short_8: LPFCGR5B

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/LPFCGR5BY5CT4PHZCTYDY3BIOL \
  | 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: 5bca2347a1c7453e3cf914f03c6c2872f4ddd07072897900c7f977071061e244

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6de75e05643474e7b3b23416227633171562dd42ef7c7d9cd1e401f175121061",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-06-01T12:22:53Z",
    "title_canon_sha256": "3c796bd1f1365c9e623a2699be01e4072c581a54114290fa7c1cdc82c459a9bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02159",
    "kind": "arxiv",
    "version": 1
  }
}