Pith Number

pith:WYG2NK4E

pith:2015:WYG2NK4EEI6PJKMBLWBAUNDRB3

not attested not anchored not stored refs pending

Chromatic thresholds in dense random graphs

Julia B\"ottcher, Peter Allen, Robert Morris, Simon Griffiths, Yoshiharu Kohayakawa

arxiv:1508.03870 v2 · 2015-08-16 · 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{WYG2NK4EEI6PJKMBLWBAUNDRB3}

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	2026-05-18T01:09:12.677761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b60da6ab84223cf4a9815d820a34710eed79a5d45fab3727ca2ddf177fd22e36

Aliases

arxiv: 1508.03870 · arxiv_version: 1508.03870v2 · doi: 10.48550/arxiv.1508.03870 · pith_short_12: WYG2NK4EEI6P · pith_short_16: WYG2NK4EEI6PJKMB · pith_short_8: WYG2NK4E

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/WYG2NK4EEI6PJKMBLWBAUNDRB3 \
  | 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: b60da6ab84223cf4a9815d820a34710eed79a5d45fab3727ca2ddf177fd22e36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e58ac2477612a4968d9a266326573eae32c0e6af1c0e2ae2da73aa925fb2bf2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-16T21:52:36Z",
    "title_canon_sha256": "d95c9f9e08e1c7f2e7cdc7b061f48204483a2eb85f2e6643ce76ba57a12068dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03870",
    "kind": "arxiv",
    "version": 2
  }
}