Pith Number

pith:XWBDUK3P

pith:2013:XWBDUK3PZPV77O2MV6F3PQBCM7

not attested not anchored not stored refs pending

Multiple phase transitions in long-range first-passage percolation on square lattices

Partha S. Dey, Shirshendu Chatterjee

arxiv:1309.5757 v2 · 2013-09-23 · 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{XWBDUK3PZPV77O2MV6F3PQBCM7}

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	2026-05-18T02:25:49.288694Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd823a2b6fcbebffbb4caf8bb7c02267de81a07d57472fc6ae4a0387741df195

Aliases

arxiv: 1309.5757 · arxiv_version: 1309.5757v2 · doi: 10.48550/arxiv.1309.5757 · pith_short_12: XWBDUK3PZPV7 · pith_short_16: XWBDUK3PZPV77O2M · pith_short_8: XWBDUK3P

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/XWBDUK3PZPV77O2MV6F3PQBCM7 \
  | 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: bd823a2b6fcbebffbb4caf8bb7c02267de81a07d57472fc6ae4a0387741df195

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29907f06d0996bdae9ff5742ad434908e58d52704bd83d1f7385e28c22d16942",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-09-23T10:41:06Z",
    "title_canon_sha256": "635756a88be273ff8ec0322c084d6c5d374ee190ec68dfc6d7f9e7e5379c3b4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5757",
    "kind": "arxiv",
    "version": 2
  }
}