Pith Number

pith:7IWYK23F

pith:2026:7IWYK23FGKX53QDZ3WRAQVQNKL

not attested not anchored not stored refs pending

Uniform Mixing in Chiral Quantum Walks

Benjamin Mustico, Christino Tamon, Gabriel Tucker, Hanmeng Zhan, Jessy Jacob Mesapam, Luke Levine

Unitary signings allow complete graphs to achieve probabilistic uniform mixing in continuous-time quantum walks.

arxiv:2605.04414 v2 · 2026-05-06 · math.CO · 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{7IWYK23FGKX53QDZ3WRAQVQNKL}

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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.

Claims

C1strongest claim

For some unitary signing σ the complete graph K^σ_n has probabilistic uniform mixing. There are infinite families of oriented circulants with average uniform mixing, a chiral violation of Godsil's No-Go theorem.

C2weakest assumption

The existence of a suitable unitary signing σ or orientation that satisfies the local uniform mixing condition via the stopping rule technique; the paper assumes the quantum walk model on these signed graphs behaves as described without additional decoherence or implementation constraints.

C3one line summary

Signed complete graphs and oriented circulants exhibit uniform mixing in quantum walks, providing a chiral violation of Godsil's no-go theorem for average mixing.

Receipt and verification

First computed	2026-05-20T00:04:34.269044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa2d856b6532afddc079dda208560d52db897a84944431639ce6473d76040055

Aliases

arxiv: 2605.04414 · arxiv_version: 2605.04414v2 · doi: 10.48550/arxiv.2605.04414 · pith_short_12: 7IWYK23FGKX5 · pith_short_16: 7IWYK23FGKX53QDZ · pith_short_8: 7IWYK23F

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/7IWYK23FGKX53QDZ3WRAQVQNKL \
  | 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: fa2d856b6532afddc079dda208560d52db897a84944431639ce6473d76040055

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f2ddded99182a35d6ccc4539c4bec21fd5a802b7b45c7566b30f8cb366be641",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-06T02:12:09Z",
    "title_canon_sha256": "7152a3b56ddde927f1058083f51b5b1af41f47e88ed6534f5068222cbff04a2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04414",
    "kind": "arxiv",
    "version": 2
  }
}