Pith Number

pith:PAF2PSHM

pith:2026:PAF2PSHMXRYZP7RBO2UTY3G4DV

not attested not anchored not stored refs pending

State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization

Jaehong Moon

A state-dependent Lyapunov method with quadratic certificates proves global convergence for gradient descent on rank-1 matrix factorization by deriving the certificates from structural axioms rather than ad hoc constructions.

arxiv:2604.26993 v2 · 2026-04-28 · math.NA · cs.LG · cs.NA · math.OC

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\usepackage{pith}
\pithnumber{PAF2PSHMXRYZP7RBO2UTY3G4DV}

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Record completeness

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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

In the certified regime, this mechanism yields convergence to a global minimizer; in the post-critical regime, it forces trajectories toward a terminal balanced manifold. The certificates arise from the monotonicity structure of the dynamics, rather than from ad hoc algebraic constructions.

C2weakest assumption

The structural axioms of the state-dependent Lyapunov framework hold, allowing the scalar certificate to be uniquely determined by local Lagrange analysis that constrains the signal and noise blocks of rank-1 extensions.

C3one line summary

Receipt and verification

First computed	2026-06-09T01:05:18.407481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

780ba7c8ecbc7197fe2176a93c6cdc1d408c0ca1e40f7cf5618c1da20b1e647e

Aliases

arxiv: 2604.26993 · arxiv_version: 2604.26993v2 · doi: 10.48550/arxiv.2604.26993 · pith_short_12: PAF2PSHMXRYZ · pith_short_16: PAF2PSHMXRYZP7RB · pith_short_8: PAF2PSHM

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/PAF2PSHMXRYZP7RBO2UTY3G4DV \
  | 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: 780ba7c8ecbc7197fe2176a93c6cdc1d408c0ca1e40f7cf5618c1da20b1e647e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f601bf87523541510699dcaac0f7f62227046a47e22bdeafb8da9b1ee831460e",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-04-28T22:43:16Z",
    "title_canon_sha256": "1a6fa78e280becc1250413c6a63b768c1bcd28010b75827d680a804f62b8d94d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26993",
    "kind": "arxiv",
    "version": 2
  }
}