Pith Number

pith:OPGR6KIJ

pith:2025:OPGR6KIJ7I6FK4YFDJDBXUGQ4I

not attested not anchored not stored refs pending

Incidence bounds related to circular Furstenberg sets

John Green, Kevin Ren, Sarah Tammen, Terence L. J. Harris, Yumeng Ou

arxiv:2502.10686 v1 · 2025-02-15 · math.CA · math.AP · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OPGR6KIJ7I6FK4YFDJDBXUGQ4I}

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.

Cited by

1 paper in Pith

Furstenberg set theorem for transversal families of functions

Receipt and verification

First computed	2026-07-05T10:14:56.463992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73cd1f2909fa3c5573051a461bd0d0e22c9862b62412319b90e2d249c980c605

Aliases

arxiv: 2502.10686 · arxiv_version: 2502.10686v1 · doi: 10.48550/arxiv.2502.10686 · pith_short_12: OPGR6KIJ7I6F · pith_short_16: OPGR6KIJ7I6FK4YF · pith_short_8: OPGR6KIJ

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/OPGR6KIJ7I6FK4YFDJDBXUGQ4I \
  | 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: 73cd1f2909fa3c5573051a461bd0d0e22c9862b62412319b90e2d249c980c605

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c53ed50ecf78441fd5fcd2dab51a7b0b9efddf9884ab92e2cd52e6ede5d5d0e",
    "cross_cats_sorted": [
      "math.AP",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-02-15T06:13:01Z",
    "title_canon_sha256": "a3c8cae2c67934cbaae7ef6e3b0b586e2eb74fceba2a237d1a3d70d37f45af63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.10686",
    "kind": "arxiv",
    "version": 1
  }
}