Pith Number

pith:W5HSRR45

pith:2025:W5HSRR45LTCHV7VCXSHTCZCSXQ

not attested not anchored not stored refs pending

Loops, not groups: Long cycles are responsible for discontinuous phase transitions in higher-order network contagions

Laurent H\'ebert-Dufresne, Leah A. Keating

arxiv:2511.15688 v2 · 2025-11-19 · physics.soc-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W5HSRR45LTCHV7VCXSHTCZCSXQ}

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	2026-06-30T00:15:08.394198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b74f28c79d5cc47afea2bc8f316452bc01c6b89c18548faa32d7f689626ab311

Aliases

arxiv: 2511.15688 · arxiv_version: 2511.15688v2 · doi: 10.48550/arxiv.2511.15688 · pith_short_12: W5HSRR45LTCH · pith_short_16: W5HSRR45LTCHV7VC · pith_short_8: W5HSRR45

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/W5HSRR45LTCHV7VCXSHTCZCSXQ \
  | 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: b74f28c79d5cc47afea2bc8f316452bc01c6b89c18548faa32d7f689626ab311

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3e4b92d7c492499bf1b0c0b8319ce1f3e97b18802bd885c4bf691738ef69b29",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2025-11-19T18:42:46Z",
    "title_canon_sha256": "b079e08faf6a777a158a4dce3ebefb5130642941758d51e5eaaea2a4a3a05fbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.15688",
    "kind": "arxiv",
    "version": 2
  }
}