Pith Number

pith:YEM7BR34

pith:2025:YEM7BR34LLOD24NAC7FTM52I5E

not attested not anchored not stored refs pending

Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

G. Soares, N. Bebiano, R. Lemos

arxiv:2508.12039 v1 · 2025-08-16 · 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{YEM7BR34LLOD24NAC7FTM52I5E}

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.

Receipt and verification

First computed	2026-07-05T11:54:59.152984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c119f0c77c5adc3d71a017cb367748e939409d4ef2b54fd45de198eec9bc6a42

Aliases

arxiv: 2508.12039 · arxiv_version: 2508.12039v1 · doi: 10.48550/arxiv.2508.12039 · pith_short_12: YEM7BR34LLOD · pith_short_16: YEM7BR34LLOD24NA · pith_short_8: YEM7BR34

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/YEM7BR34LLOD24NAC7FTM52I5E \
  | 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: c119f0c77c5adc3d71a017cb367748e939409d4ef2b54fd45de198eec9bc6a42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a10c0741a1b5d64a34a314783b82e872aa16b6c450add1b5e8a45af294a63249",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-08-16T13:27:24Z",
    "title_canon_sha256": "dce2826614aebf25d543d559cfef7ca46226c72e0103f54ca81d6a13d34a0832"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.12039",
    "kind": "arxiv",
    "version": 1
  }
}