Pith Number

pith:Y5X643LG

pith:2026:Y5X643LGHIPUJ2OYMGNRD4ZJXN

not attested not anchored not stored refs pending

Vector valued de Branges spaces, CNU contractions and functional models

Bharti Garg, Santanu Sarkar

Vector valued de Branges spaces provide functional models for completely non-unitary contractions with matching characteristic functions.

arxiv:2604.10686 v2 · 2026-04-12 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5X643LGHIPUJ2OYMGNRD4ZJXN}

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

We show that these spaces provide functional models for certain completely non-unitary contraction operators. In particular, we show that the characteristic function coincides with the projection operator valued function on the unit disc.

C2weakest assumption

A suitable direct sum decomposition of the Hilbert space exists that produces reproducing kernels satisfying the de Branges space axioms for the given pair of Fredholm operator-valued analytic functions.

C3one line summary

Vector-valued de Branges spaces built from operator-valued analytic functions provide functional models for CNU contractions, with the Sz.-Nagy-Foias characteristic function coinciding with a projection-valued function on the unit disk.

Receipt and verification

First computed	2026-06-04T01:09:49.735301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c76fee6d663a1f44e9d8619b11f329bb7f06b116a187090bddd4cb4fc7517d2c

Aliases

arxiv: 2604.10686 · arxiv_version: 2604.10686v2 · doi: 10.48550/arxiv.2604.10686 · pith_short_12: Y5X643LGHIPU · pith_short_16: Y5X643LGHIPUJ2OY · pith_short_8: Y5X643LG

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/Y5X643LGHIPUJ2OYMGNRD4ZJXN \
  | 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: c76fee6d663a1f44e9d8619b11f329bb7f06b116a187090bddd4cb4fc7517d2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a47310ef01c60e41981e627dbd5d900fad98bbb6d75416cbd00990c782ede976",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-04-12T15:24:44Z",
    "title_canon_sha256": "a0b09223f73828fc028504b41c90f5a9a2e6e9d50e5dbbb9c8e0ac6e3ceabb3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.10686",
    "kind": "arxiv",
    "version": 2
  }
}