Pith Number

pith:NJHGQQ3H

pith:2026:NJHGQQ3HZTMRPHDDSDS7LBCSWC

not attested not anchored not stored refs pending

Proof of the Holevo--Utkin conjecture on sharp $\ell_p$ norms for zero-sum vectors

Haonan Zhang

The conjectured sharp bounds on p-norm to 2-norm ratios for zero-sum vectors hold for all dimensions four and higher.

arxiv:2605.05243 v2 · 2026-05-04 · math.CA · math-ph · math.FA · math.MP

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\usepackage{pith}
\pithnumber{NJHGQQ3HZTMRPHDDSDS7LBCSWC}

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Record completeness

1 Bitcoin timestamp

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

For d ≥ 4 the minimum of ||x||_p / ||x||_2 over non-zero zero-sum x equals 2^{1/p-1/2} when 0 < p ≤ 1, equals the min of that quantity and ((d-1)^{p/2} + (d-1)^{1-p/2})/d^{p/2})^{1/p} when 1 < p < 2, and the analogous maximum statement holds for q > 2.

C2weakest assumption

The proof must correctly identify and compare the two candidate extremal configurations (the two-support vector and the equitable (d-1)-support vector) and show no other zero-sum vector yields a smaller or larger ratio; this case analysis is not visible in the abstract.

C3one line summary

Proves that the minimum and maximum of ||x||_p / ||x||_2 over non-zero zero-sum x in R^d equal the stated closed-form expressions for all d ≥ 4.

Receipt and verification

First computed	2026-05-22T01:04:04.510376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a4e684367ccd9179c6390e5f58452b09f6d9b02ad4c972350d04dbd0e6c6cae

Aliases

arxiv: 2605.05243 · arxiv_version: 2605.05243v2 · doi: 10.48550/arxiv.2605.05243 · pith_short_12: NJHGQQ3HZTMR · pith_short_16: NJHGQQ3HZTMRPHDD · pith_short_8: NJHGQQ3H

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/NJHGQQ3HZTMRPHDDSDS7LBCSWC \
  | 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: 6a4e684367ccd9179c6390e5f58452b09f6d9b02ad4c972350d04dbd0e6c6cae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ad62238a58ea42fcf9f43ba600934df88735f8a5b6c1a57b08aca32d767e405",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-04T03:11:54Z",
    "title_canon_sha256": "9cf4a152028ac9498483138188955fadc2bed8a15e0f04fe952d6c2d0f561efd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.05243",
    "kind": "arxiv",
    "version": 2
  }
}