Pith Number

pith:L7VCRMSK

pith:2026:L7VCRMSKICK5D2PUJPG2KHAP25

not attested not anchored not stored refs pending

Greedy sparsifications of sums of positive semidefinite matrices

Grigory Ivanov

There exists a deterministic sequence of positive semidefinite matrices whose partial averages converge to the identity with explicit error bounds in operator norm.

arxiv:2604.06439 v2 · 2026-04-07 · math.FA

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\usepackage{pith}
\pithnumber{L7VCRMSKICK5D2PUJPG2KHAP25}

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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

✓ Portable graph bundle live · download bundle · merged state

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

We show that there exists a deterministic sequence of indices i1,i2,… such that for every integer k≥1, ||(1/k) sum_{r=1}^k A_{ir} - I_d|| ≤ 2M ln(2d)/k if k ≤ M ln(2d), and ≤ 3 sqrt(M ln(2d)/k) otherwise.

C2weakest assumption

The result assumes there exist lambda_i ≥0 summing to 1 with sum lambda_i A_i = I_d and ||A_i||≤M for all i; if no such convex combination exists, the theorem gives no information. The proof must also construct or guarantee the sequence under only these hypotheses.

C3one line summary

There exists a deterministic sequence of the given PSD matrices such that the k-term average deviates from the identity by at most 2M ln(2d)/k when k is small and 3 sqrt(M ln(2d)/k) when k is large, enabling epsilon-approximations with N = O(M log d / eps^2) terms.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:04:01.627509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fea28b24a4095d1e9f44bcda51c0fd7595ed6c1668d57560b66d4a6f4882e76

Aliases

arxiv: 2604.06439 · arxiv_version: 2604.06439v2 · doi: 10.48550/arxiv.2604.06439 · pith_short_12: L7VCRMSKICK5 · pith_short_16: L7VCRMSKICK5D2PU · pith_short_8: L7VCRMSK

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/L7VCRMSKICK5D2PUJPG2KHAP25 \
  | 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: 5fea28b24a4095d1e9f44bcda51c0fd7595ed6c1668d57560b66d4a6f4882e76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4551d89704857983af055547baa8a0bd36826494c69a5cfaf8d1ab6d28c9db77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-04-07T20:28:22Z",
    "title_canon_sha256": "de3a4a85f7c05e6796f29681e7986944ee950ad82e5334c7eb9084acb25c241d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06439",
    "kind": "arxiv",
    "version": 2
  }
}