Pith Number

pith:44EPKUN5

pith:2025:44EPKUN5JAZGGPAIETQJ2BUNST

not attested not anchored not stored refs pending

Fully Dynamic Spectral and Cut Sparsifiers for Directed Graphs

Yibin Zhao

arxiv:2507.19632 v1 · 2025-07-25 · 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{44EPKUN5JAZGGPAIETQJ2BUNST}

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	2026-07-05T11:43:37.998637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e708f551bd4832633c0824e09d068d94f4e4b95f1b88d83b284abbe9bc802de0

Aliases

arxiv: 2507.19632 · arxiv_version: 2507.19632v1 · doi: 10.48550/arxiv.2507.19632 · pith_short_12: 44EPKUN5JAZG · pith_short_16: 44EPKUN5JAZGGPAI · pith_short_8: 44EPKUN5

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/44EPKUN5JAZGGPAIETQJ2BUNST \
  | 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: e708f551bd4832633c0824e09d068d94f4e4b95f1b88d83b284abbe9bc802de0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad51140cb0b82aa52e43c7d9931409cdc668e0ae4a1b8a63c6d573a96e34142e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2025-07-25T18:59:47Z",
    "title_canon_sha256": "7570b4e22db1850fdde2b1171a8d458ed3f687a5f033c2188d121a0cc4949f82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.19632",
    "kind": "arxiv",
    "version": 1
  }
}