Pith Number

pith:SZGCEVVW

pith:2015:SZGCEVVWMYPPTXNCXKRYM5P42I

not attested not anchored not stored refs pending

Computing Walrasian Equilibria: Fast Algorithms and Structural Properties

Renato Paes Leme, Sam Chiu-wai Wong

arxiv:1511.04032 v2 · 2015-11-12 · cs.GT · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SZGCEVVWMYPPTXNCXKRYM5P42I}

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	2026-05-18T01:17:43.067418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

964c2256b6661ef9dda2baa38675fcd21f31482296f16359803e8b907811860c

Aliases

arxiv: 1511.04032 · arxiv_version: 1511.04032v2 · doi: 10.48550/arxiv.1511.04032 · pith_short_12: SZGCEVVWMYPP · pith_short_16: SZGCEVVWMYPPTXNC · pith_short_8: SZGCEVVW

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/SZGCEVVWMYPPTXNCXKRYM5P42I \
  | 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: 964c2256b6661ef9dda2baa38675fcd21f31482296f16359803e8b907811860c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0116d9e3fd87b15737c7f9bbe48de8a5d0cf7ac136e9556de0adc2d0e21d4fd7",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2015-11-12T19:51:23Z",
    "title_canon_sha256": "81d0db61411c713d3fd208696fab315233ad1cf3adf8f6b86f2fec587c682fb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04032",
    "kind": "arxiv",
    "version": 2
  }
}