Pith Number

pith:JPKIDMFI

pith:2026:JPKIDMFIPAUSMCQENG2WJ5IURW

not attested not anchored not stored refs resolved

Conformal Rigidity of Graphs: Subdifferentials and Orbit-Isometries

Andrew Niu

A single eigenvector certifies conformal rigidity for vertex-transitive graphs and similar symmetric ones.

arxiv:2605.15017 v1 · 2026-05-14 · math.CO · math.OC · math.SP

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\pithnumber{JPKIDMFIPAUSMCQENG2WJ5IURW}

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1 Bitcoin timestamp

2 Internet Archive

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

for a large class of graphs, including all vertex-transitive ones, we show that conformal rigidity is certified by a single eigenvector, resolving an open question and explaining the conformal rigidity of previously unexplained graphs.

C2weakest assumption

The assumption that edge-isometric spectral embeddings characterize conformal rigidity (unified here with the subdifferential perspective) and that the orbit-isometric weakening remains sufficient.

C3one line summary

A subdifferential framework certifies conformal rigidity via orbit-isometric embeddings, reducing the problem for vertex-transitive graphs to a single-eigenvector check and in general to linear feasibility or Gröbner bases.

References

48 extracted · 48 resolved · 0 Pith anchors

[1] Catherine Babecki, Stefan Steinerberger, and Rekha R. Thomas. Spectrahedral geometry of graph sparsifiers.SIAM J. Discrete Math., 39(1):449–483, 2025 2025

[2] Laugesen.Symmetrization in analysis 2019

[3] MPS/SIAM Series on Optimization 2001

[4] A survey of maximalk-degenerate graphs andk-trees.Theory and Applications of Graphs, 0(1):Article 5, 2024 2024

[5] Jacek Bochnak, Michel Coste, and Marie-Fran¸ coise Roy.Real algebraic geometry. Transl. from the French., volume 36 ofErgeb. Math. Grenzgeb., 3. Folge. Berlin: Springer, rev. and updated ed. edition, 1998

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:54.716976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bd481b0a87829260a0469b564f5148db0dd593d35c845e6969c59ff24309f0e

Aliases

arxiv: 2605.15017 · arxiv_version: 2605.15017v1 · doi: 10.48550/arxiv.2605.15017 · pith_short_12: JPKIDMFIPAUS · pith_short_16: JPKIDMFIPAUSMCQE · pith_short_8: JPKIDMFI

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/JPKIDMFIPAUSMCQENG2WJ5IURW \
  | 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: 4bd481b0a87829260a0469b564f5148db0dd593d35c845e6969c59ff24309f0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c7b3826caafc71df2598e6749e3d81434083f8bd0d1667856d7a050cbacac3e",
    "cross_cats_sorted": [
      "math.OC",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T16:18:40Z",
    "title_canon_sha256": "2520e2583bbaa0d3f97b87a8c8df3f4c2399a943e06e47b1bc60f7509deb3777"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15017",
    "kind": "arxiv",
    "version": 1
  }
}