Pith Number

pith:ISXCEQ6Q

pith:2016:ISXCEQ6QB2KVOK3VLPDOV7ZRRY

not attested not anchored not stored refs pending

Expander Graph and Communication-Efficient Decentralized Optimization

Tianyu Wu, Wei Shi, Wotao Yin, Yat-Tin Chow

arxiv:1612.00903 v1 · 2016-12-03 · math.OC · cs.DC · cs.MA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ISXCEQ6QB2KVOK3VLPDOV7ZRRY}

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	2026-05-18T00:55:53.849538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44ae2243d00e95572b755bc6eaff318e33fda87ae5def07356a98d1b0c8693ed

Aliases

arxiv: 1612.00903 · arxiv_version: 1612.00903v1 · doi: 10.48550/arxiv.1612.00903 · pith_short_12: ISXCEQ6QB2KV · pith_short_16: ISXCEQ6QB2KVOK3V · pith_short_8: ISXCEQ6Q

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/ISXCEQ6QB2KVOK3VLPDOV7ZRRY \
  | 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: 44ae2243d00e95572b755bc6eaff318e33fda87ae5def07356a98d1b0c8693ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9d548189764cf4da61a14cce70a6c158fb025caaab2bf7d25970e7272ce954f",
    "cross_cats_sorted": [
      "cs.DC",
      "cs.MA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-12-03T00:36:50Z",
    "title_canon_sha256": "86a31c13f0897b2ca32955abc40edada121d73d5565504c9f5b6f8fb953fc78b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00903",
    "kind": "arxiv",
    "version": 1
  }
}