Pith Number

pith:GIUL5Q3S

pith:2026:GIUL5Q3SNT4FZLIQ2FRINTXLBF

not attested not anchored not stored refs pending

Covariant formulation of the Berry connection in non-Hermitian systems

Ievgen I. Arkhipov

The metric tensor of the Hilbert space defines a unique Hermitian Berry connection for non-Hermitian systems that remains covariant under arbitrary GL(N,C) frame transformations.

arxiv:2601.19777 v4 · 2026-01-27 · quant-ph · cond-mat.mes-hall · cond-mat.quant-gas

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\pithnumber{GIUL5Q3SNT4FZLIQ2FRINTXLBF}

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Record completeness

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4 Citations 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 resulting covariant Berry connection is uniquely defined, Hermitian, and covariant under arbitrary GL(N,C) frame transformations, while recovering the standard Berry connection in the Hermitian limit.

C2weakest assumption

That the metric tensor of the Hilbert space supplies the correct structure to decouple eigenbundle geometry from the metric and remove all gauge ambiguities without introducing new ones or depending on additional choices.

C3one line summary

A metric-tensor-based covariant formalism uniquely defines the Berry connection in non-Hermitian systems, resolving GL(N,C) gauge ambiguities and enabling consistent geometric phases and topological invariants.

Receipt and verification

First computed	2026-06-03T01:05:48.110219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3228bec3726cf85cad10d16286ceeb0974c870187c17604f6c5ba7e9499433fa

Aliases

arxiv: 2601.19777 · arxiv_version: 2601.19777v4 · doi: 10.48550/arxiv.2601.19777 · pith_short_12: GIUL5Q3SNT4F · pith_short_16: GIUL5Q3SNT4FZLIQ · pith_short_8: GIUL5Q3S

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GIUL5Q3SNT4FZLIQ2FRINTXLBF \
  | 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: 3228bec3726cf85cad10d16286ceeb0974c870187c17604f6c5ba7e9499433fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14d96a3c2007c6d2bc3701fea75c9a769ec072d142047b4ba9cd3f4ad3fce6cf",
    "cross_cats_sorted": [
      "cond-mat.mes-hall",
      "cond-mat.quant-gas"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-01-27T16:40:52Z",
    "title_canon_sha256": "ec4c4fc9431cb085af51fbb041632c07aa89b5a1f06fbbf3a5a21c2a7cb96527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.19777",
    "kind": "arxiv",
    "version": 4
  }
}