Pith Number

pith:Q6ED4XOF

pith:2026:Q6ED4XOFM2R4R7AQWLEJYV6T27

not attested not anchored not stored refs pending

On the Perelman-Pukhov quotient of successive radii: better and asymptotically optimal bounds

Beatriz Mar\'in Gimeno, Bernardo Gonz\'alez Merino, Mia Runge

arxiv:2606.30241 v1 · 2026-06-29 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q6ED4XOFM2R4R7AQWLEJYV6T27}

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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	2026-06-30T02:17:55.739586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87883e5dc566a3c8fc10b2c89c57d3d7f0c5b9bef6e243eaeac1fda1906a1ad8

Aliases

arxiv: 2606.30241 · arxiv_version: 2606.30241v1 · doi: 10.48550/arxiv.2606.30241 · pith_short_12: Q6ED4XOFM2R4 · pith_short_16: Q6ED4XOFM2R4R7AQ · pith_short_8: Q6ED4XOF

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/Q6ED4XOFM2R4R7AQWLEJYV6T27 \
  | 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: 87883e5dc566a3c8fc10b2c89c57d3d7f0c5b9bef6e243eaeac1fda1906a1ad8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a58c1458f27b4f497c38fb7c7eb33904b4763dca56502ac05fe3387dc5d3c7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-06-29T12:52:10Z",
    "title_canon_sha256": "37cdf65d3332c4c1184b27d264509ffa7c513497e84732ee49987ba4fe5e344c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30241",
    "kind": "arxiv",
    "version": 1
  }
}