Pith Number

pith:W2J3U2GL

pith:2026:W2J3U2GLFORUNBLPNVRALDPKPV

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Topological Classification of Insulators: III. Non-interacting Spectrally-Gapped Systems in All Dimensions

Jacob Shapiro, Jui-Hui Chung

The space of gapped Hamiltonians has path-connected components exactly matching the strong topological invariants in all dimensions and symmetry classes.

arxiv:2602.12512 v3 · 2026-02-13 · math-ph · math.FA · math.MP · math.OA

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\pithnumber{W2J3U2GLFORUNBLPNVRALDPKPV}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

The strong topological invariants become complete invariants yielding the Kitaev periodic table, now derived as the set of path-connected components of the space of Hamiltonians.

C2weakest assumption

The chosen notions of locality and bulk non-triviality on the space of Hamiltonians are the natural ones that make the strong invariants complete; if a different notion of locality is required by physics, the classification may change.

C3one line summary

Strong topological invariants are complete invariants for the path-connected components of the space of spectrally gapped non-interacting Hamiltonians across all dimensions and Altland-Zirnbauer classes.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

The Zak phase in topologically insulating chains: invariants and limitations

Receipt and verification

First computed	2026-05-26T02:05:07.040325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b693ba68cb2ba346856f6d62058dea7d6be070588a847f389115773d137af59c

Aliases

arxiv: 2602.12512 · arxiv_version: 2602.12512v3 · doi: 10.48550/arxiv.2602.12512 · pith_short_12: W2J3U2GLFORU · pith_short_16: W2J3U2GLFORUNBLP · pith_short_8: W2J3U2GL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W2J3U2GLFORUNBLPNVRALDPKPV \
  | 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: b693ba68cb2ba346856f6d62058dea7d6be070588a847f389115773d137af59c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bc063d3af3bee058d513912c7cb26217131c0e815d87a96b76e4206d13d27a8",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-02-13T01:30:28Z",
    "title_canon_sha256": "d26b10b57f8628c4c4ff674cf3ebf7c846a4e5df3c92b3c64c3d26384f70859b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.12512",
    "kind": "arxiv",
    "version": 3
  }
}