Pith Number

pith:4SFVKVCL

pith:2026:4SFVKVCLXBYW46RFS4TOQIRUUW

not attested not anchored not stored refs pending

Separating Geodesic Structure and Product Structure

Laura Merker, Lena Scherzer, Samuel Schneider

arxiv:2607.02098 v1 · 2026-07-02 · math.CO · cs.DM · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4SFVKVCLXBYW46RFS4TOQIRUUW}

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	2026-07-03T01:17:42.227073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e48b55544bb8716e7a259726e82234a5bb7ff00f3fd42088c6d67a746e2a3d5b

Aliases

arxiv: 2607.02098 · arxiv_version: 2607.02098v1 · doi: 10.48550/arxiv.2607.02098 · pith_short_12: 4SFVKVCLXBYW · pith_short_16: 4SFVKVCLXBYW46RF · pith_short_8: 4SFVKVCL

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/4SFVKVCLXBYW46RFS4TOQIRUUW \
  | 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: e48b55544bb8716e7a259726e82234a5bb7ff00f3fd42088c6d67a746e2a3d5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7889e1e19221ec5f9c76a4afbc74aade1c83d11e8fcfc7bd3544945b91579e5",
    "cross_cats_sorted": [
      "cs.DM",
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-02T12:34:27Z",
    "title_canon_sha256": "891e82be9653cf98f6bea2642e4c394079360a8c126e74f548d41af7a2180028"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02098",
    "kind": "arxiv",
    "version": 1
  }
}