Pith Number

pith:JULFSBCL

pith:2026:JULFSBCLLAIYQYZUTQECCZAMQ7

not attested not anchored not stored refs pending

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

Quentin Berger, Shuta Nakajima

arxiv:2605.30707 v1 · 2026-05-29 · 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{JULFSBCLLAIYQYZUTQECCZAMQ7}

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	2026-06-01T01:03:09.559643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d1659044b58118863349c0821640c87e6e43b7838af67d76f14329fbaebaa5a

Aliases

arxiv: 2605.30707 · arxiv_version: 2605.30707v1 · doi: 10.48550/arxiv.2605.30707 · pith_short_12: JULFSBCLLAIY · pith_short_16: JULFSBCLLAIYQYZU · pith_short_8: JULFSBCL

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/JULFSBCLLAIYQYZUTQECCZAMQ7 \
  | 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: 4d1659044b58118863349c0821640c87e6e43b7838af67d76f14329fbaebaa5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8e27d84cb47e0fe8f32ddbc6d45786fe951ee9416bd0350e82b8c6452ebfb3d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-29T00:58:44Z",
    "title_canon_sha256": "1af37e189fc1cbe44c8fc401f29d57229102a471f3915ed730fbcffa1e8d06bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.30707",
    "kind": "arxiv",
    "version": 1
  }
}