Pith Number

pith:ILECLDZ7

pith:2026:ILECLDZ7NXXLHKJN2AZ42IPMHX

not attested not anchored not stored refs pending

Rigidity and Structural Asymmetry of Bounded Solutions

Walid Oukil

If solutions for both s and 1-conjugate(s) are bounded on [1,∞) then Re(s) must equal 1/2.

arxiv:2603.15716 v4 · 2026-03-16 · math.DS

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\usepackage{pith}
\pithnumber{ILECLDZ7NXXLHKJN2AZ42IPMHX}

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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

if two solutions with the same initial condition equal to 1, corresponding respectively to the parameters s and 1−s̄ lying in the critical strip, are both bounded on [1,+∞), then Re(s) = 1/2.

C2weakest assumption

The rotation number hypothesis imposed on the non-homogeneous term, which is required to establish the structural asymmetry between s and 1-conjugate(s).

C3one line summary

Bounded solutions for parameters s and 1-conjugate(s) imply Re(s) = 1/2 under the rotation number hypothesis on the non-homogeneous term.

Receipt and verification

First computed	2026-05-20T01:05:11.245946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42c8258f3f6deeb3a92dd033cd21ec3dc4818f4b8991dcf01c48bb64f8282046

Aliases

arxiv: 2603.15716 · arxiv_version: 2603.15716v4 · doi: 10.48550/arxiv.2603.15716 · pith_short_12: ILECLDZ7NXXL · pith_short_16: ILECLDZ7NXXLHKJN · pith_short_8: ILECLDZ7

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/ILECLDZ7NXXLHKJN2AZ42IPMHX \
  | 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: 42c8258f3f6deeb3a92dd033cd21ec3dc4818f4b8991dcf01c48bb64f8282046

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "146119799795dba37d9d49d797d69bcd50b4f82689325c6d0a826b410f9331fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-03-16T15:45:16Z",
    "title_canon_sha256": "dbd4482d4a60eb1e622fb0908c1b02ce3c69e9bfd2f2a49a06d5b6caa786424a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.15716",
    "kind": "arxiv",
    "version": 4
  }
}