Pith Number

pith:6BT75TS3

pith:2026:6BT75TS3SLH5DGWCUYBMRT3GEW

not attested not anchored not stored refs pending

Isomorphic Busemann--Petty for arbitrary measures: the sharp order

Alexander Koldobsky, Artem Zvavitch

arxiv:2608.02098 v1 · 2026-08-03 · 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{6BT75TS3SLH5DGWCUYBMRT3GEW}

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	2026-08-04T02:10:50.555787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f067fece5b92cfd19ac2a602c8cf6625bfa541b6666de527c4eca294f7ca136c

Aliases

arxiv: 2608.02098 · arxiv_version: 2608.02098v1 · doi: 10.48550/arxiv.2608.02098 · pith_short_12: 6BT75TS3SLH5 · pith_short_16: 6BT75TS3SLH5DGWC · pith_short_8: 6BT75TS3

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/6BT75TS3SLH5DGWCUYBMRT3GEW \
  | 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: f067fece5b92cfd19ac2a602c8cf6625bfa541b6666de527c4eca294f7ca136c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcf1cf88f0f5c220fbc0e25f294523c00cfc3a84dcdc74ab8880c935794c26cd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-08-03T11:59:41Z",
    "title_canon_sha256": "d549036c1715d59c526dcb323d9ab5927c5053ce2892b70c2386a71f3207a73b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.02098",
    "kind": "arxiv",
    "version": 1
  }
}