Pith Number

pith:EZB4AL6F

pith:2026:EZB4AL6FWKEWUEGU2ZGOTED24J

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Ordered POVMs and Residual Collapse

James Tian

A residual transform on ordered POVM realizations produces a collapsed form with mutually orthogonal non-escape coordinates whose supports strongly sum to the identity.

arxiv:2605.17592 v1 · 2026-05-17 · math.FA · math-ph · math.MP · quant-ph · stat.ME

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Record completeness

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Claims

C1strongest claim

The resulting collapse map gives an equivalence relation on ordered POVM realizations. Its range consists of collapsed POVMs, whose non-escape coordinates are mutually orthogonal and whose support projections strongly sum to the identity. The fiber over a collapsed POVM consists of all ordered realizations with the same residually visible compressions.

C2weakest assumption

Under natural hypotheses, iterating the transform produces a collapsed POVM whose non-escape coordinates are the parts of the original effects that survive all earlier tests.

C3one line summary

Defines a residual collapse map for ordered POVMs that produces collapsed POVMs with mutually orthogonal non-escape coordinates and characterizes the map's range and fibers.

References

34 extracted · 34 resolved · 0 Pith anchors

[1] Takesaki, M. , date-added =. Theory of operator algebras

[2] Douglas, R. G. , date-added =. On majorization, factorization, and range inclusion of operators on. Proc. Amer. Math. Soc. , mrclass =. 1966 , bdsk-url-1 =. doi:10.2307/2035178 , fjournal = 1966 · doi:10.2307/2035178

[3] Methods of modern mathematical physics

[4] Probabilistic and Statistical Aspects of Quantum Theory 2011 · doi:10.1007/978-88-7642-378-9

[5] Holevo, A. S. , date-added =. Statistical decision theory for quantum systems , url =. J. Multivariate Anal. , mrclass =. 1973 , bdsk-url-1 =. doi:10.1016/0047-259X(73)90028-6 , fjournal = 1973 · doi:10.1016/0047-259x(73)90028-6

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:47.634067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2643c02fc5b2896a10d4d64ce9907ae25a0513821a4af415ffc24e49192df073

Aliases

arxiv: 2605.17592 · arxiv_version: 2605.17592v1 · doi: 10.48550/arxiv.2605.17592 · pith_short_12: EZB4AL6FWKEW · pith_short_16: EZB4AL6FWKEWUEGU · pith_short_8: EZB4AL6F

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EZB4AL6FWKEWUEGU2ZGOTED24J \
  | 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: 2643c02fc5b2896a10d4d64ce9907ae25a0513821a4af415ffc24e49192df073

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3632e50bdea81bff50ef319f1da2d6d0fc3f9dddc01dca550c1b90c12a9756e7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph",
      "stat.ME"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-17T18:39:47Z",
    "title_canon_sha256": "287c10868f9284854c418f1c3a52e0aec835103fd8c888c324fa7a01a38c5f6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17592",
    "kind": "arxiv",
    "version": 1
  }
}