Pith Number

pith:MPLQWPYX

pith:2025:MPLQWPYXA76SM64RW6B2DLACKL

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Distinguishing finite metric spaces via similarity spectra

Jun O'Hara

The q-spectrum from similarity matrices distinguishes all finite metric spaces on at most four points and a large class of larger ones.

arxiv:2502.08980 v6 · 2025-02-13 · math.MG

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\usepackage{pith}
\pithnumber{MPLQWPYXA76SM64RW6B2DLACKL}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

The q-spectrum completely distinguishes a large class of finite metric spaces and all metric spaces on at most 4 points. The transition q-spectrum distinguishes spaces for which the multiset of pairwise distances is independent over the rational numbers, along with all spaces on at most 3 points.

C2weakest assumption

The similarity matrices are constructed so that their spectra encode enough metric information to separate the claimed classes; the paper invokes this construction without an independent verification that the matrix definition is the minimal or canonical choice that preserves distinction power.

C3one line summary

Introduces q-spectrum and transition q-spectrum invariants for finite metric spaces that recover graph spectra in a limit and distinguish all spaces with at most 4 and 3 points respectively under stated conditions.

Receipt and verification

First computed	2026-06-02T01:03:30.516901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63d70b3f1707fd267b91b783a1ac0252fcdc263976e59587dd8ce2afe0df7381

Aliases

arxiv: 2502.08980 · arxiv_version: 2502.08980v6 · doi: 10.48550/arxiv.2502.08980 · pith_short_12: MPLQWPYXA76S · pith_short_16: MPLQWPYXA76SM64R · pith_short_8: MPLQWPYX

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/MPLQWPYXA76SM64RW6B2DLACKL \
  | 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: 63d70b3f1707fd267b91b783a1ac0252fcdc263976e59587dd8ce2afe0df7381

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a8f3766d4f9fb00a11c99778c5e32ff1e99f9f636bd6e1b9acbdfd70c0502fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2025-02-13T05:33:41Z",
    "title_canon_sha256": "db668bfb0416403e8971d56d2e1694abc268511ab59fabea9f6e5eb42f050a03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.08980",
    "kind": "arxiv",
    "version": 6
  }
}