Pith Number

pith:BF7R3VN4

pith:2017:BF7R3VN4YNVAMHSWA4IRZ4OUXD

not attested not anchored not stored refs pending

An upper bound for the critical probability on the Cartesian product graph of a regular tree and a line

Kohei Yamamoto

arxiv:1705.06873 v4 · 2017-05-19 · 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{BF7R3VN4YNVAMHSWA4IRZ4OUXD}

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	2026-05-18T00:17:54.747696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

097f1dd5bcc36a061e5607111cf1d4b8cb6cd0dd8849d989e5d4a61e6180847a

Aliases

arxiv: 1705.06873 · arxiv_version: 1705.06873v4 · doi: 10.48550/arxiv.1705.06873 · pith_short_12: BF7R3VN4YNVA · pith_short_16: BF7R3VN4YNVAMHSW · pith_short_8: BF7R3VN4

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/BF7R3VN4YNVAMHSWA4IRZ4OUXD \
  | 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: 097f1dd5bcc36a061e5607111cf1d4b8cb6cd0dd8849d989e5d4a61e6180847a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2270d61d9602555d40dc2047928e3ad9ca4d2e23d9850dfe43efd01d96e4677b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-05-19T06:50:07Z",
    "title_canon_sha256": "86e5eaa3f05d08679e60e3940fbfd6b5be27dc1c766805dd6783306e1cfe09db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.06873",
    "kind": "arxiv",
    "version": 4
  }
}