Pith Number

pith:ZVLWYF65

pith:2026:ZVLWYF65HWKQYWCRBDPF6T65I2

not attested not anchored not stored refs pending

A Complete Equational Presentation of Qudit Circuits via Polycontrolled PROPs

Colin Blake

A finite, dimension-uniform equational theory is given that is sound and complete for all exact unitary qudit circuits.

arxiv:2602.09873 v3 · 2026-02-10 · quant-ph · cs.LO

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\usepackage{pith}
\pithnumber{ZVLWYF65HWKQYWCRBDPF6T65I2}

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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

We give the first finite schematic equational theory that is sound and complete for exact unitary qudit circuits in every finite dimension at least two.

C2weakest assumption

That the chosen primitive value-control operation, together with the diagrammatic PROP structure, is sufficient to generate all controlled operations from local rules without introducing dimension-dependent axioms.

C3one line summary

A finite, dimension-uniform equational theory is given that is sound and complete for all exact unitary qudit circuits.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-26T01:15:49.340880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd576c17dd3d950c585108de5f4fdd46ac9d416de6a5b3e996ddcf82a656b07e

Aliases

arxiv: 2602.09873 · arxiv_version: 2602.09873v3 · doi: 10.48550/arxiv.2602.09873 · pith_short_12: ZVLWYF65HWKQ · pith_short_16: ZVLWYF65HWKQYWCR · pith_short_8: ZVLWYF65

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/ZVLWYF65HWKQYWCRBDPF6T65I2 \
  | 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: cd576c17dd3d950c585108de5f4fdd46ac9d416de6a5b3e996ddcf82a656b07e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05a812b62046bf76442c736451b01e9f523bbc73bef605f4cad05c32d5586bf9",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-02-10T15:16:46Z",
    "title_canon_sha256": "21fb57ed2b943ddd7c6a860d6276b21b5147e9addc4e3059cde9a0a243e465c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.09873",
    "kind": "arxiv",
    "version": 3
  }
}