Pith Number

pith:2JEJRDO4

pith:2025:2JEJRDO4WDE4FT7YTJAJT3YMFP

not attested not anchored not stored refs pending

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition

Anders Aamand, Justin Y. Chen, Mina Dalirrooyfard, Sandeep Silwal, Slobodan Mitrovi\'c, Yinzhan Xu, Yuriy Nevmyvaka

arxiv:2507.01873 v1 · 2025-07-02 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2JEJRDO4WDE4FT7YTJAJT3YMFP}

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	2026-07-05T11:30:57.285405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d248988ddcb0c9c2cff89a4099ef0c2bddba7ac89e0e628805df0fac3c5c90cc

Aliases

arxiv: 2507.01873 · arxiv_version: 2507.01873v1 · doi: 10.48550/arxiv.2507.01873 · pith_short_12: 2JEJRDO4WDE4 · pith_short_16: 2JEJRDO4WDE4FT7Y · pith_short_8: 2JEJRDO4

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/2JEJRDO4WDE4FT7YTJAJT3YMFP \
  | 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: d248988ddcb0c9c2cff89a4099ef0c2bddba7ac89e0e628805df0fac3c5c90cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "736f523b824f5568a070ff66cef97e9982c17417b0d4352011636a2927d14522",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2025-07-02T16:38:51Z",
    "title_canon_sha256": "eb028e5f875c4eff192569d0fb50f4edbffa5684c4d1bc3479522d565309816a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.01873",
    "kind": "arxiv",
    "version": 1
  }
}