Pith Number

pith:PKHJPPUS

pith:2026:PKHJPPUSMHM76Y7CII5MZ6NH2S

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Discrete Mixed Quantization

Qiaochu Ma

A mixed quantization technique defined on graph vector bundles advances the analysis of multiple asymptotic spectral problems including the Alon-Boppana bound and quantum ergodicity.

arxiv:2605.16203 v1 · 2026-05-15 · math.SP · math-ph · math.DG · math.MP

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Record completeness

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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

We develop a mixed quantization technique for graph vector bundles and apply it to several asymptotic spectral problems, including the Alon-Boppana bound, the Kesten-McKay law, quantum ergodicity, zero divisor convergence, and Ramanujan vector bundles.

C2weakest assumption

That a consistent mixed quantization can be defined on graph vector bundles in a way that preserves the necessary spectral properties for the listed asymptotic analyses to hold without additional unstated conditions.

C3one line summary

Develops mixed quantization for graph vector bundles and applies it to asymptotic spectral problems including Alon-Boppana bound, Kesten-McKay law, and quantum ergodicity.

References

81 extracted · 81 resolved · 0 Pith anchors

[1] N. Alon. Eigenvalues and expanders. volume 6, pages 83–96. 1986. Theory of com- puting (Singer Island, Fla., 1984) 1986

[2] Anantharaman 2017

[3] Anantharaman 2022

[4] N. Anantharaman and E. Le Masson. Quantum ergodicity on large regular graphs. Duke Math. J. , 164(4):723–765, 2015 2015

[5] N. Anantharaman and M. Sabri. Quantum ergodicity on graphs: from spectral to spatial delocalization. Ann. of Math. (2) , 189(3):753–835, 2019 2019

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:57.838000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a8e97be9261d9ff63e2423accf9a7d4a36f43a6f799886bee0c00440e7a6dad

Aliases

arxiv: 2605.16203 · arxiv_version: 2605.16203v1 · doi: 10.48550/arxiv.2605.16203 · pith_short_12: PKHJPPUSMHM7 · pith_short_16: PKHJPPUSMHM76Y7C · pith_short_8: PKHJPPUS

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/PKHJPPUSMHM76Y7CII5MZ6NH2S \
  | 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: 7a8e97be9261d9ff63e2423accf9a7d4a36f43a6f799886bee0c00440e7a6dad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3ed3df80d76c342bbe9427602818645efcdab6600f186168afb12f4c3087a7e",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-05-15T17:21:17Z",
    "title_canon_sha256": "b119e745afe6508b15636de4dc3ac33487e48192eba042aa5bd444de2b2ffbb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16203",
    "kind": "arxiv",
    "version": 1
  }
}