Pith Number

pith:X6DULCYJ

pith:2026:X6DULCYJTKB6ACGYXKEM4Y5OHS

not attested not anchored not stored refs pending

From Morse Trees to $J$-Holomorphic Discs -- Rigid Y-Graphs

Erkao Bao, Ke Zhu

arxiv:2606.09054 v1 · 2026-06-08 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6DULCYJTKB6ACGYXKEM4Y5OHS}

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	2026-06-09T02:07:55.942174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf87458b099a83e008d8ba88ce63ae3c9cccf0deb9ee8a57355733a894e871fa

Aliases

arxiv: 2606.09054 · arxiv_version: 2606.09054v1 · doi: 10.48550/arxiv.2606.09054 · pith_short_12: X6DULCYJTKB6 · pith_short_16: X6DULCYJTKB6ACGY · pith_short_8: X6DULCYJ

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/X6DULCYJTKB6ACGYXKEM4Y5OHS \
  | 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: bf87458b099a83e008d8ba88ce63ae3c9cccf0deb9ee8a57355733a894e871fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a32ae6fc6a232d3a45892a9a0d050c077d40dc5bda56fcd7e878efd5f67f45fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2026-06-08T05:42:29Z",
    "title_canon_sha256": "e7363069229254d24e83b2676aef9e9ae7ee6eea9462f310a66efd7bd9e82052"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09054",
    "kind": "arxiv",
    "version": 1
  }
}