Pith Number

pith:YHQVDUWE

pith:2026:YHQVDUWEJC3AYDXWVJTH4JR3HF

not attested not anchored not stored refs pending

Paradoxes of Game Theoretic Equilibria and Price of Anarchy

Georgios Piliouras, Ian Gemp, Luke Marris, Siqi Liu

arxiv:2607.11752 v1 · 2026-07-13 · cs.GT · cs.LG · cs.MA · math.DS · 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{YHQVDUWEJC3AYDXWVJTH4JR3HF}

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	2026-07-14T02:22:22.900120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1e151d2c448b60c0ef6aa667e263b39737c3bb6ac7c9e7d24ecd62a859ee6fe

Aliases

arxiv: 2607.11752 · arxiv_version: 2607.11752v1 · doi: 10.48550/arxiv.2607.11752 · pith_short_12: YHQVDUWEJC3A · pith_short_16: YHQVDUWEJC3AYDXW · pith_short_8: YHQVDUWE

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/YHQVDUWEJC3AYDXWVJTH4JR3HF \
  | 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: c1e151d2c448b60c0ef6aa667e263b39737c3bb6ac7c9e7d24ecd62a859ee6fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6c7b48a59253389f159e65f22dc8b5fe7302e8ed87c6f9d75ca127e220873c7",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.MA",
      "math.DS",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-07-13T16:09:35Z",
    "title_canon_sha256": "913cd83a7c4889d581cfa5efd20090d89b1336806f34f78819244c6676dff503"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11752",
    "kind": "arxiv",
    "version": 1
  }
}