Pith Number

pith:MGDPHDWD

pith:2010:MGDPHDWDWQJISTDK6KYL4WA3AO

not attested not anchored not stored refs pending

Improved Social Welfare Bounds for GSP at Equilibrium

Brendan Lucier, Renato Paes Leme

arxiv:1011.3268 v1 · 2010-11-14 · 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{MGDPHDWDWQJISTDK6KYL4WA3AO}

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	2026-05-18T04:35:56.199192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6186f38ec3b412894c6af2b0be581b03b76221d8dc00834b862cabbb7140a6c0

Aliases

arxiv: 1011.3268 · arxiv_version: 1011.3268v1 · doi: 10.48550/arxiv.1011.3268 · pith_short_12: MGDPHDWDWQJI · pith_short_16: MGDPHDWDWQJISTDK · pith_short_8: MGDPHDWD

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/MGDPHDWDWQJISTDK6KYL4WA3AO \
  | 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: 6186f38ec3b412894c6af2b0be581b03b76221d8dc00834b862cabbb7140a6c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e5f16560b893f562abcdc4e14f15fc59dfd3bbf0619f6395caeb1694194e4e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2010-11-14T23:53:27Z",
    "title_canon_sha256": "b651b10a858d1910df5c3ecf230b6fabd36ae15073467195f4f7173d435ceb97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3268",
    "kind": "arxiv",
    "version": 1
  }
}