Pith Number

pith:RPLYQWRW

pith:2026:RPLYQWRWR7DJMHUAILKDZLHDO2

not attested not anchored not stored refs pending

Average hitting times and recurrence structures II: Cartesian products of powers of cycles and regular graphs

Shunya Tamura, Tsuyoshi Miezaki

arxiv:2608.11734 v1 · 2026-08-12 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RPLYQWRWR7DJMHUAILKDZLHDO2}

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	2026-08-13T01:27:57.536275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8bd7885a368fc6961e8042d43cace3768fac08815bd3f1f5340b488ba362721b

Aliases

arxiv: 2608.11734 · arxiv_version: 2608.11734v1 · doi: 10.48550/arxiv.2608.11734 · pith_short_12: RPLYQWRWR7DJ · pith_short_16: RPLYQWRWR7DJMHUA · pith_short_8: RPLYQWRW

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/RPLYQWRWR7DJMHUAILKDZLHDO2 \
  | 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: 8bd7885a368fc6961e8042d43cace3768fac08815bd3f1f5340b488ba362721b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48a3b669eaea44712eb257897ff1ce08c0e9b84a7b0d76446a2b246a3aec7d84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-12T07:13:16Z",
    "title_canon_sha256": "8ea175552d43cb82d5683a5393c9c3d52e177fa4ac0816e7d5258832f2c825c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.11734",
    "kind": "arxiv",
    "version": 1
  }
}