Pith Number

pith:C2CZEYLS

pith:2026:C2CZEYLS4JYPL74ETKNOPM4MVU

not attested not anchored not stored refs pending

Sharp spectral constants for scaled $q$-numerical ranges

Mohamed Amine Aouichaoui, Ryan O'Loughlin

arxiv:2608.09866 v1 · 2026-08-10 · 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{C2CZEYLS4JYPL74ETKNOPM4MVU}

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	2026-08-11T02:25:17.859790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1685926172e270f5ff849a9ae7b38cad20dbe5b251d54e7dbc39c1b82b3b34be

Aliases

arxiv: 2608.09866 · arxiv_version: 2608.09866v1 · doi: 10.48550/arxiv.2608.09866 · pith_short_12: C2CZEYLS4JYP · pith_short_16: C2CZEYLS4JYPL74E · pith_short_8: C2CZEYLS

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/C2CZEYLS4JYPL74ETKNOPM4MVU \
  | 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: 1685926172e270f5ff849a9ae7b38cad20dbe5b251d54e7dbc39c1b82b3b34be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "712bc6b553172635265b1e95635058fa500f80201a5d14b697e12fcb2e4ce6c5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-08-10T17:23:51Z",
    "title_canon_sha256": "175baec8f1d31316d7f9ce0248bfbb7bc886d19470c8e81d7548d3d7bb2a7bae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09866",
    "kind": "arxiv",
    "version": 1
  }
}