Pith Number

pith:RU3ZT7QJ

pith:2025:RU3ZT7QJSWLG4YSXQTMKMP2EEI

not attested not anchored not stored refs pending

The Triangle Friendship Paradox

Bishakh Bhattacharya, Frank den Hollander, Nitya Gadhiwala, Pradeeptha R Jain, Tejashree Subramanya

arxiv:2507.02627 v1 · 2025-07-03 · 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{RU3ZT7QJSWLG4YSXQTMKMP2EEI}

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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.

Cited by

1 paper in Pith

Large deviation principle for friendship-biases in Galton--Watson trees

Receipt and verification

First computed	2026-07-05T11:31:31.991541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d3799fe0995966e625784d8a63f442232807f68a92e353a781cd5deb6aa7c6c

Aliases

arxiv: 2507.02627 · arxiv_version: 2507.02627v1 · doi: 10.48550/arxiv.2507.02627 · pith_short_12: RU3ZT7QJSWLG · pith_short_16: RU3ZT7QJSWLG4YSX · pith_short_8: RU3ZT7QJ

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/RU3ZT7QJSWLG4YSXQTMKMP2EEI \
  | 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: 8d3799fe0995966e625784d8a63f442232807f68a92e353a781cd5deb6aa7c6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d428630b6020cdb94a882a83e425002f9b9f0bfc0f939cc9eb6d7d0d72781640",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-03T13:53:20Z",
    "title_canon_sha256": "868552ca3ad8d579793b5cbf59e11b1831ecde3001489e397350cb39a6cf0cee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.02627",
    "kind": "arxiv",
    "version": 1
  }
}