Pith Number

pith:PSPBLDOA

pith:2009:PSPBLDOANIHG7DY5BHTXAR6T4B

not attested not anchored not stored refs pending

Sharp threshold functions for the random intersection graph via coupling method?

Katarzyna Rybarczyk

arxiv:0910.0749 v2 · 2009-10-05 · 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{PSPBLDOANIHG7DY5BHTXAR6T4B}

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	2026-05-18T03:37:20.488821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c9e158dc06a0e6f8f1d09e77047d3e04b35a73c57333db690246e94506f1e2f

Aliases

arxiv: 0910.0749 · arxiv_version: 0910.0749v2 · doi: 10.48550/arxiv.0910.0749 · pith_short_12: PSPBLDOANIHG · pith_short_16: PSPBLDOANIHG7DY5 · pith_short_8: PSPBLDOA

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/PSPBLDOANIHG7DY5BHTXAR6T4B \
  | 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: 7c9e158dc06a0e6f8f1d09e77047d3e04b35a73c57333db690246e94506f1e2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d34ffaf446dbecc9abbac4159bd36fe5b80f27535986161e9015af31365960b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-10-05T12:34:44Z",
    "title_canon_sha256": "f0fbcb24db4f83846ad0510741dc2ed4c5664cbfed8a6f054300b2741336a7a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.0749",
    "kind": "arxiv",
    "version": 2
  }
}