Pith Number

pith:BPTS4OZI

pith:2018:BPTS4OZIN5VV2ZLSRAZURQGXPY

not attested not anchored not stored refs pending

A lower bound for the number of elastic collisions

Krzysztof Burdzy, Mauricio Duarte

arxiv:1803.00979 v2 · 2018-03-02 · math.DS · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BPTS4OZIN5VV2ZLSRAZURQGXPY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-17T23:50:28.478622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0be72e3b286f6b5d6572883348c0d77e20bdf222e5a3c2bb4e2364a2d6ba4066

Aliases

arxiv: 1803.00979 · arxiv_version: 1803.00979v2 · doi: 10.48550/arxiv.1803.00979 · pith_short_12: BPTS4OZIN5VV · pith_short_16: BPTS4OZIN5VV2ZLS · pith_short_8: BPTS4OZI

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/BPTS4OZIN5VV2ZLSRAZURQGXPY \
  | 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: 0be72e3b286f6b5d6572883348c0d77e20bdf222e5a3c2bb4e2364a2d6ba4066

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e718dbb4d981783217138f38fbe5603674b78ddba35f9c9b7e0ba7017c40bd4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-03-02T18:14:49Z",
    "title_canon_sha256": "2536d5a388c94a05f8e75b4574d17f0b19c37c0fc2079bc753e7c411d3b61ca3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.00979",
    "kind": "arxiv",
    "version": 2
  }
}