Pith Number

pith:RGG7LQCN

pith:2026:RGG7LQCN2BI7YLOIWPMJM3CYOO

not attested not anchored not stored refs pending

On the crossing number of knots and links on surface in 3-manifolds

Tetsuya Ito

arxiv:2606.18776 v1 · 2026-06-17 · 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{RGG7LQCN2BI7YLOIWPMJM3CYOO}

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	2026-06-19T16:11:46.995710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

898df5c04dd051fc2dc8b3d8966c5873abe8e0a6cdf5fcb068a1654cea53725c

Aliases

arxiv: 2606.18776 · arxiv_version: 2606.18776v1 · doi: 10.48550/arxiv.2606.18776 · pith_short_12: RGG7LQCN2BI7 · pith_short_16: RGG7LQCN2BI7YLOI · pith_short_8: RGG7LQCN

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/RGG7LQCN2BI7YLOIWPMJM3CYOO \
  | 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: 898df5c04dd051fc2dc8b3d8966c5873abe8e0a6cdf5fcb068a1654cea53725c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ce4a1177d0677849f8ebea82b56f31c640e73f972f9f89faa47eec7a54af59b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-06-17T07:39:14Z",
    "title_canon_sha256": "40dafcaf6c9cd233b7eb90c4466f4fd7fc6e5b4136051e1a6f4a99c16e947564"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18776",
    "kind": "arxiv",
    "version": 1
  }
}