Pith Number

pith:5EOSKBM2

pith:2011:5EOSKBM2XFSWPHJ5F4NQBP6JHB

not attested not anchored not stored refs pending

A copolymer near a selective interface: variational characterization of the free energy

A.A. Opoku, E. Bolthausen, F. den Hollander

arxiv:1110.1315 v2 · 2011-10-06 · 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{5EOSKBM2XFSWPHJ5F4NQBP6JHB}

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	2026-05-18T04:02:01.751695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e91d25059ab965679d3d2f1b00bfc93853c1e1e38979689d13c3980daab2a2f3

Aliases

arxiv: 1110.1315 · arxiv_version: 1110.1315v2 · doi: 10.48550/arxiv.1110.1315 · pith_short_12: 5EOSKBM2XFSW · pith_short_16: 5EOSKBM2XFSWPHJ5 · pith_short_8: 5EOSKBM2

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/5EOSKBM2XFSWPHJ5F4NQBP6JHB \
  | 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: e91d25059ab965679d3d2f1b00bfc93853c1e1e38979689d13c3980daab2a2f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78ae8f8bf2cc9dc8dbea99cc9044258a4659608d4365a2d228961f87547b55d1",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-06T16:41:52Z",
    "title_canon_sha256": "347cdea904c613cabbe42c9e9eeb6524570993d11e5ff2df5d46f15a4d936c2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1315",
    "kind": "arxiv",
    "version": 2
  }
}