Pith Number

pith:K2YISSWG

pith:2026:K2YISSWGEZ6ZGCRAVMH3DHL4AX

not attested not anchored not stored refs pending

Structural aspects of extremal functions in the Krzy\.z conjecture

Sullivan F. MacDonald

Extremal functions for the Krzyż conjecture must have at least a positive fraction of n atoms if they are atomic singular inner functions.

arxiv:2605.08411 v2 · 2026-05-08 · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K2YISSWGEZ6ZGCRAVMH3DHL4AX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

Extremal functions for the nth coefficient in the Krzyż conjecture are atomic singular inner functions with at most n atoms. This paper gives a lower bound on the number of atoms N of the form N≥cn, marking progress toward proving the expected N=n.

C2weakest assumption

The assumption, stated as given in the abstract, that extremal functions are atomic singular inner functions; if this classification fails for some n, the lower bound and equivalent conditions derived from it would not apply.

C3one line summary

Extremal functions in the Krzyż conjecture have at least cn atoms, with new variational formulas and equivalent conditions for the conjecture.

Receipt and verification

First computed	2026-05-20T02:05:44.860079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56b0894ac6267d930a20ab0fb19d7c05f538d7d13ee11e86177e48f937d1f44d

Aliases

arxiv: 2605.08411 · arxiv_version: 2605.08411v2 · doi: 10.48550/arxiv.2605.08411 · pith_short_12: K2YISSWGEZ6Z · pith_short_16: K2YISSWGEZ6ZGCRA · pith_short_8: K2YISSWG

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/K2YISSWGEZ6ZGCRAVMH3DHL4AX \
  | 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: 56b0894ac6267d930a20ab0fb19d7c05f538d7d13ee11e86177e48f937d1f44d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4b72f4a5b92c0d89a9bf6bcf7f337be77a800cfed83c06cdb5c07781d50af72",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-05-08T19:17:48Z",
    "title_canon_sha256": "6b85bf735043ac316e67acc665e317bccfe3aed581049b33cdb867366dc8a477"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08411",
    "kind": "arxiv",
    "version": 2
  }
}