Pith Number

pith:5MDVI3KU

pith:2026:5MDVI3KUZIHLUPXKE6XCI4UREY

not attested not anchored not stored refs pending

Tracks on planar complexes and soficity

Hiroki Ishikura

arxiv:2606.08279 v1 · 2026-06-06 · math.CO · math.DS · math.GR · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5MDVI3KUZIHLUPXKE6XCI4UREY}

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	2026-06-09T01:05:32.069595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb07546d54ca0eba3eea27ae24729126358895dd0908b2e27417b03c989bc4b2

Aliases

arxiv: 2606.08279 · arxiv_version: 2606.08279v1 · doi: 10.48550/arxiv.2606.08279 · pith_short_12: 5MDVI3KUZIHL · pith_short_16: 5MDVI3KUZIHLUPXK · pith_short_8: 5MDVI3KU

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/5MDVI3KUZIHLUPXKE6XCI4UREY \
  | 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: eb07546d54ca0eba3eea27ae24729126358895dd0908b2e27417b03c989bc4b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2b314860e675cf7da2f0b20f18416de64087af01194164855e7602393e32553",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-06T17:57:47Z",
    "title_canon_sha256": "f1fad7d65e92eeb467793b2336daf3d0910aeff92764a80e90e3fd6687383d2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08279",
    "kind": "arxiv",
    "version": 1
  }
}