Pith Number

pith:6XFUWEVZ

pith:2025:6XFUWEVZOOQITLTQSYDVJBKS3M

not attested not anchored not stored refs pending

Discrete Poincar\'e inequalities and universal approximators for random graphs

Dylan J. Altschuler, Konstantinos Tyros, Konstantin Tikhomirov, Pandelis Dodos

arxiv:2506.17433 v2 · 2025-06-20 · math.MG · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6XFUWEVZOOQITLTQSYDVJBKS3M}

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	2026-07-05T11:45:36.669250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5cb4b12b973a089ae709607548552db2c3aee237bae57d314ced92356bef3c7

Aliases

arxiv: 2506.17433 · arxiv_version: 2506.17433v2 · doi: 10.48550/arxiv.2506.17433 · pith_short_12: 6XFUWEVZOOQI · pith_short_16: 6XFUWEVZOOQITLTQ · pith_short_8: 6XFUWEVZ

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/6XFUWEVZOOQITLTQSYDVJBKS3M \
  | 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: f5cb4b12b973a089ae709607548552db2c3aee237bae57d314ced92356bef3c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9093d999bdcbc068e40f52090ccbe98bd52011a3ccdb829e143e5ab7be5de9af",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2025-06-20T18:55:09Z",
    "title_canon_sha256": "677e15fe43fc66cf788bca42ca3f7479096e76ea2141b63aa2fd0f7175be657c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.17433",
    "kind": "arxiv",
    "version": 2
  }
}