Pith Number

pith:A2EBNYNF

pith:2025:A2EBNYNFJFFGRADD3GGM5LLXAJ

not attested not anchored not stored refs pending

The localization transition for the directed polymer in a random environment is smooth

Hubert Lacoin

arxiv:2505.13382 v1 · 2025-05-19 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A2EBNYNFJFFGRADD3GGM5LLXAJ}

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.

Cited by

1 paper in Pith

Sharp behavior of the free energy for the two-dimensional directed polymer model

Receipt and verification

First computed	2026-07-05T11:05:29.277392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

068816e1a5494a688063d98ccead770248bb2ff7f5ecb9d50bd1a3864e418088

Aliases

arxiv: 2505.13382 · arxiv_version: 2505.13382v1 · doi: 10.48550/arxiv.2505.13382 · pith_short_12: A2EBNYNFJFFG · pith_short_16: A2EBNYNFJFFGRADD · pith_short_8: A2EBNYNF

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/A2EBNYNFJFFGRADD3GGM5LLXAJ \
  | 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: 068816e1a5494a688063d98ccead770248bb2ff7f5ecb9d50bd1a3864e418088

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f7fa1d783fb4b304d1b110441221aa00131a79ff963bf0b803346a8ea1d55f5",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-05-19T17:25:15Z",
    "title_canon_sha256": "27192de82aeeb5eb2fff077f66ad726727a667a405acce1053455399ceda5ef2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.13382",
    "kind": "arxiv",
    "version": 1
  }
}