Pith Number

pith:BY4ZFBJN

pith:2025:BY4ZFBJNLYMXBN6MX25SKMBORZ

not attested not anchored not stored refs pending

Erd\H{o}s's unit distance problem and rigidity

J\'anos Pach, J\'ozsef Solymosi, Orit E. Raz

arxiv:2507.15679 v1 · 2025-07-21 · 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{BY4ZFBJNLYMXBN6MX25SKMBORZ}

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	2026-07-05T11:40:41.882334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e3992852d5e1970b7ccbebb25302e8e4981e3f78386fbe5c91b8ac0147a7a52

Aliases

arxiv: 2507.15679 · arxiv_version: 2507.15679v1 · doi: 10.48550/arxiv.2507.15679 · pith_short_12: BY4ZFBJNLYMX · pith_short_16: BY4ZFBJNLYMXBN6M · pith_short_8: BY4ZFBJN

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/BY4ZFBJNLYMXBN6MX25SKMBORZ \
  | 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: 0e3992852d5e1970b7ccbebb25302e8e4981e3f78386fbe5c91b8ac0147a7a52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8eb27b88b805e102e0ff21c854ecc89162cc7f39eaf3705b6665526fbada2212",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-21T14:43:01Z",
    "title_canon_sha256": "8cb7a22b71cff39ca120883b9e33ac51a1b4d0352b504207332efb09dbd2232b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15679",
    "kind": "arxiv",
    "version": 1
  }
}