Pith Number

pith:EDH7E5OW

pith:2015:EDH7E5OWLW76JNHCWIPM6W42KZ

not attested not anchored not stored refs pending

Two-parameter version of Bourgain's inequality: Rational frequencies

Bartosz Trojan, Ben Krause, Mariusz Mirek

arxiv:1504.04132 v1 · 2015-04-16 · math.CA · 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{EDH7E5OWLW76JNHCWIPM6W42KZ}

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	2026-05-18T02:18:39.733848Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20cff275d65dbfe4b4e2b21ecf5b9a5672db2735dd6cb60e2d903e75b77df5f3

Aliases

arxiv: 1504.04132 · arxiv_version: 1504.04132v1 · doi: 10.48550/arxiv.1504.04132 · pith_short_12: EDH7E5OWLW76 · pith_short_16: EDH7E5OWLW76JNHC · pith_short_8: EDH7E5OW

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/EDH7E5OWLW76JNHCWIPM6W42KZ \
  | 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: 20cff275d65dbfe4b4e2b21ecf5b9a5672db2735dd6cb60e2d903e75b77df5f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8d7777061fb5bf75a92d8f4f3f91359cfc13e468ff82ad2b0ec66cd91f83e14",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-04-16T08:21:29Z",
    "title_canon_sha256": "b35cd3c021d36db64d9ec845ed82527e0b69a9d42dc6113db8cc51fde268e9cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04132",
    "kind": "arxiv",
    "version": 1
  }
}