Pith Number

pith:7DP6GBBU

pith:2019:7DP6GBBUVEWS7DI2SLBQJBRWWM

not attested not anchored not stored refs pending

Upper tail bounds for cycles

Abigail Raz

arxiv:1903.07488 v2 · 2019-03-18 · 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{7DP6GBBUVEWS7DI2SLBQJBRWWM}

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	2026-05-17T23:49:38.494923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8dfe30434a92d2f8d1a92c3048636b310d1f01429d680b292473d019e3e841b

Aliases

arxiv: 1903.07488 · arxiv_version: 1903.07488v2 · doi: 10.48550/arxiv.1903.07488 · pith_short_12: 7DP6GBBUVEWS · pith_short_16: 7DP6GBBUVEWS7DI2 · pith_short_8: 7DP6GBBU

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/7DP6GBBUVEWS7DI2SLBQJBRWWM \
  | 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: f8dfe30434a92d2f8d1a92c3048636b310d1f01429d680b292473d019e3e841b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebcd4257d11f27a0fcbfc7a752d347488e9b651c476bea8eb0ed69533940086b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-18T14:49:22Z",
    "title_canon_sha256": "ca2214986e545c3f2fc14cd7e3ecb3211a6abc642ff564ffe2b8f36e3ceb4e72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.07488",
    "kind": "arxiv",
    "version": 2
  }
}