Pith Number

pith:5VL4RDLL

pith:2026:5VL4RDLLNPGQ6CZAHZGBM6I23X

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Categorical (Co)Limits of Quantum Graphs

Jennifer Zhu

Quantum graphs are identified with left ideals in the extended Haagerup tensor product to give representation-free morphisms and categorical colimits.

arxiv:2605.13019 v1 · 2026-05-13 · math.OA · math.CT

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Claims

C1strongest claim

Using these left ideals and some operator space theory, we find a new, representation-free characterization of a morphism of quantum graphs compatible with previous representation-dependent morphisms. A notion of categorical (co)limit of quantum graphs follows.

C2weakest assumption

That left ideals in the extended Haagerup tensor product M ⊗_eh M provide a canonical complement to a quantum graph and that this correspondence yields morphisms compatible with all prior representation-dependent definitions.

C3one line summary

Quantum graphs are redefined as left ideals in the extended Haagerup tensor product, enabling representation-independent morphisms and categorical (co)limits.

References

15 extracted · 15 resolved · 1 Pith anchors

[1] The quantum-to- classical graph homomorphism game 2022 · doi:10.1063/5.0072288(cit

[2] The Dual of the Haagerup Tensor Prod- uct 2004

[3] onlinelibrary · doi:10.1112/jlms/s2-45.1.126(cit

[4] Connectivity for Quantum Graphs via Quantum Adjacency Operators 2025 · doi:10.1007/978-3-031-

[5] Zero-Error Communica- tion via Quantum Channels, Noncommutative Graphs, and a Quantum Lov´ asz Number 2013 · doi:10.1109/tit.2012.2221677.url:http://dx.doi

Formal links

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Receipt and verification

First computed	2026-05-18T03:09:00.071413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed57c88d6b6bcd0f0b203e4c16791adde8e41387dcb50ef9bc3a7bc220d0b40a

Aliases

arxiv: 2605.13019 · arxiv_version: 2605.13019v1 · doi: 10.48550/arxiv.2605.13019 · pith_short_12: 5VL4RDLLNPGQ · pith_short_16: 5VL4RDLLNPGQ6CZA · pith_short_8: 5VL4RDLL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5VL4RDLLNPGQ6CZAHZGBM6I23X \
  | 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: ed57c88d6b6bcd0f0b203e4c16791adde8e41387dcb50ef9bc3a7bc220d0b40a

Canonical record JSON

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      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-13T05:21:07Z",
    "title_canon_sha256": "c0f2ee50d4ec77de339b9862ab8b7bcf6c730b59229eb5d765eada952e680e52"
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