Pith Number

pith:F6PF2HGC

pith:2009:F6PF2HGCBHLYX7VNM3OWKGC7KH

not attested not anchored not stored refs pending

Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

Alexander V Turbiner

arxiv:0907.4485 v1 · 2009-07-26 · math-ph · cond-mat.stat-mech · hep-th · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F6PF2HGCBHLYX7VNM3OWKGC7KH}

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	2026-05-18T02:12:53.490702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f9e5d1cc209d78bfead66dd65185f51ec8a9d93ad1af75e634e68412bd0e7a7

Aliases

arxiv: 0907.4485 · arxiv_version: 0907.4485v1 · doi: 10.48550/arxiv.0907.4485 · pith_short_12: F6PF2HGCBHLY · pith_short_16: F6PF2HGCBHLYX7VN · pith_short_8: F6PF2HGC

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/F6PF2HGCBHLYX7VNM3OWKGC7KH \
  | 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: 2f9e5d1cc209d78bfead66dd65185f51ec8a9d93ad1af75e634e68412bd0e7a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7c8e05218c628c521e9e2920aecced67f6b2000ce2ed1ec445f2c629a7feb69",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "hep-th",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-07-26T13:56:05Z",
    "title_canon_sha256": "db54a52b50ab40df395c1c806aca7ceb1fd4293978723bc84b2e18621dd3d43f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4485",
    "kind": "arxiv",
    "version": 1
  }
}