Pith Number

pith:YNLYLCDR

pith:2016:YNLYLCDRWMGPL6LFK3IMOVMPKZ

not attested not anchored not stored refs pending

Convex Program Duality, Fisher Markets, and Nash Social Welfare

Kamal Jain, Nikhil R. Devanur, Richard Cole, Sadra Yazdanbod, Tung Mai, Vasilis Gkatzelis, Vijay V. Vazirani

arxiv:1609.06654 v1 · 2016-09-21 · cs.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YNLYLCDRWMGPL6LFK3IMOVMPKZ}

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	2026-05-18T01:04:06.271860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c357858871b30cf5f96556d0c7558f564f6c7915c0076862e641b4bd2849d261

Aliases

arxiv: 1609.06654 · arxiv_version: 1609.06654v1 · doi: 10.48550/arxiv.1609.06654 · pith_short_12: YNLYLCDRWMGP · pith_short_16: YNLYLCDRWMGPL6LF · pith_short_8: YNLYLCDR

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/YNLYLCDRWMGPL6LFK3IMOVMPKZ \
  | 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: c357858871b30cf5f96556d0c7558f564f6c7915c0076862e641b4bd2849d261

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4229bc1a711505bfbba4aee36bad379b6ff62346be9ef4befed1483ea939a45",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2016-09-21T18:02:42Z",
    "title_canon_sha256": "8875b58bee4239c19ac1a64fa3b8619146a7bcc17a0b66d0c511a653ce3ed027"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06654",
    "kind": "arxiv",
    "version": 1
  }
}