Pith Number

pith:PE36YBVV

pith:2019:PE36YBVVNV6T466LAVARE4LTY6

not attested not anchored not stored refs pending

A phase transformation for the number of optimal paths in first passage percolation

Yu Zhang

arxiv:1905.12819 v1 · 2019-05-30 · 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{PE36YBVVNV6T466LAVARE4LTY6}

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	2026-05-17T23:44:39.578255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7937ec06b56d7d3e7bcb0541127173c7b74fb030ccfacd620633c355659df5b2

Aliases

arxiv: 1905.12819 · arxiv_version: 1905.12819v1 · doi: 10.48550/arxiv.1905.12819 · pith_short_12: PE36YBVVNV6T · pith_short_16: PE36YBVVNV6T466L · pith_short_8: PE36YBVV

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/PE36YBVVNV6T466LAVARE4LTY6 \
  | 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: 7937ec06b56d7d3e7bcb0541127173c7b74fb030ccfacd620633c355659df5b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a60b840cb4385e0f9e2365aecc7baca6a1fb8bb0e050bec2b89028f44adeb69a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-05-30T01:39:37Z",
    "title_canon_sha256": "a3892dc1a0dfcf65d68877719f354a469be70f6e5b97eb5cdaaf18dfe21bca5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.12819",
    "kind": "arxiv",
    "version": 1
  }
}