Pith Number

pith:CZ4BGWFJ

pith:2025:CZ4BGWFJ5T2DZERIZQW2CZ7GRB

not attested not anchored not stored refs pending

Magnetic Double-Wells: Absence of Tunneling

Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein

arxiv:2509.02857 v1 · 2025-09-02 · math-ph · cond-mat.mes-hall · math.AP · math.CA · math.MP · physics.atm-clus

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CZ4BGWFJ5T2DZERIZQW2CZ7GRB}

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	2026-07-05T12:03:58.587277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16781358a9ecf43c9228cc2da167e6887901b05537ea7fb46c0fc8add948cf3e

Aliases

arxiv: 2509.02857 · arxiv_version: 2509.02857v1 · doi: 10.48550/arxiv.2509.02857 · pith_short_12: CZ4BGWFJ5T2D · pith_short_16: CZ4BGWFJ5T2DZERI · pith_short_8: CZ4BGWFJ

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/CZ4BGWFJ5T2DZERIZQW2CZ7GRB \
  | 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: 16781358a9ecf43c9228cc2da167e6887901b05537ea7fb46c0fc8add948cf3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e053a8ca98ce2f2685467261e88df9f774ef014e39132d0ef43fbd1b7b8dbeb1",
    "cross_cats_sorted": [
      "cond-mat.mes-hall",
      "math.AP",
      "math.CA",
      "math.MP",
      "physics.atm-clus"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-09-02T22:04:20Z",
    "title_canon_sha256": "d143f81e66b2f4f282789c2ae8c0bd1d7c05710c1c760e0c516bc083ea9bc572"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.02857",
    "kind": "arxiv",
    "version": 1
  }
}