Pith Number

pith:VWRKPHTP

pith:2025:VWRKPHTPUV6HVZG7CISFMUZ34J

not attested not anchored not stored refs pending

Discontinuous observables as an obstruction for small essential spectral radius

Daniel Smania, Oliver Butterley

arxiv:2506.07613 v1 · 2025-06-09 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VWRKPHTPUV6HVZG7CISFMUZ34J}

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	2026-07-05T11:18:30.332223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ada2a79e6fa57c7ae4df122456533be24b44352590503e34351cd6f35238d4cc

Aliases

arxiv: 2506.07613 · arxiv_version: 2506.07613v1 · doi: 10.48550/arxiv.2506.07613 · pith_short_12: VWRKPHTPUV6H · pith_short_16: VWRKPHTPUV6HVZG7 · pith_short_8: VWRKPHTP

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/VWRKPHTPUV6HVZG7CISFMUZ34J \
  | 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: ada2a79e6fa57c7ae4df122456533be24b44352590503e34351cd6f35238d4cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "679da62e7f88cf3111e3604b4f80bf1a2d0889a79075fc9aabfbe4bf86fbab61",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-06-09T10:26:17Z",
    "title_canon_sha256": "75899a46bddb9718f008a08fecd26b7cd8183f448c0c7dacd0bcb3a1f376ea20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07613",
    "kind": "arxiv",
    "version": 1
  }
}