Pith Number

pith:BCSH3WDF

pith:2026:BCSH3WDFEXLORFOSQ7XRAIN5SL

not attested not anchored not stored refs pending

Flat minimal tori and Lu's second-gap conjecture

Fagui Li, Yuhang Zhao

arxiv:2606.30432 v1 · 2026-06-29 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BCSH3WDFEXLORFOSQ7XRAIN5SL}

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	2026-06-30T02:18:14.990588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08a47dd86525d6e895d287ef1021bd92ebb934bd56bc3754f66020f23dd9320b

Aliases

arxiv: 2606.30432 · arxiv_version: 2606.30432v1 · doi: 10.48550/arxiv.2606.30432 · pith_short_12: BCSH3WDFEXLO · pith_short_16: BCSH3WDFEXLORFOS · pith_short_8: BCSH3WDF

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/BCSH3WDFEXLORFOSQ7XRAIN5SL \
  | 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: 08a47dd86525d6e895d287ef1021bd92ebb934bd56bc3754f66020f23dd9320b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45d16ad578e95e58b28b72d13219d130ed37148f743f5e92d7d22f942a25a2d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-29T15:11:01Z",
    "title_canon_sha256": "dac061d56d8201128f5ca53dc1768c4d898bd5c8c0d899ef90a558912ea9a418"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30432",
    "kind": "arxiv",
    "version": 1
  }
}