Pith Number

pith:V4V46SZ6

pith:2026:V4V46SZ6NSHDEMGLIBOSLKIJMS

not attested not anchored not stored refs pending

Phase distinction of Gibbs states without symmetry breaking: topological invariants of the 3D toric code

Haruki Watanabe

arxiv:2607.00134 v1 · 2026-06-30 · cond-mat.str-el · cond-mat.other · cond-mat.stat-mech

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V4V46SZ6NSHDEMGLIBOSLKIJMS}

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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

Quantized topological invariant of symmetry-projected Gibbs states

Receipt and verification

First computed	2026-07-02T00:18:35.969198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af2bcf4b3e6c8e3230cb405d25a90964a3b112fd9eb1dd6238734feac1f4e5f4

Aliases

arxiv: 2607.00134 · arxiv_version: 2607.00134v1 · doi: 10.48550/arxiv.2607.00134 · pith_short_12: V4V46SZ6NSHD · pith_short_16: V4V46SZ6NSHDEMGL · pith_short_8: V4V46SZ6

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/V4V46SZ6NSHDEMGLIBOSLKIJMS \
  | 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: af2bcf4b3e6c8e3230cb405d25a90964a3b112fd9eb1dd6238734feac1f4e5f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24c4dbc1cc567ad3233fe80a40b20b1ec3e7e6ae4cd9d3ab0d277e564d758e53",
    "cross_cats_sorted": [
      "cond-mat.other",
      "cond-mat.stat-mech"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-06-30T20:12:45Z",
    "title_canon_sha256": "d2431ab606f31f3e22d13d782fc03f62f9c4e52b8111aaed05da1cd538744b01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00134",
    "kind": "arxiv",
    "version": 1
  }
}