Pith Number

pith:ELM5KNY3

pith:2026:ELM5KNY3WFXOXQUOTZDOCGNO73

not attested not anchored not stored refs pending

Beyond the PPAD hardness of Auto-bidding Auctions

Jamie Morgenstern, Li Chen, Yuanyuan Yang

arxiv:2608.01889 v1 · 2026-08-03 · 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{ELM5KNY3WFXOXQUOTZDOCGNO73}

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	2026-08-04T02:07:32.197444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22d9d5371bb16eebc28e9e46e119aefefc6db168dd6fa243175392465d7b33b7

Aliases

arxiv: 2608.01889 · arxiv_version: 2608.01889v1 · doi: 10.48550/arxiv.2608.01889 · pith_short_12: ELM5KNY3WFXO · pith_short_16: ELM5KNY3WFXOXQUO · pith_short_8: ELM5KNY3

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/ELM5KNY3WFXOXQUOTZDOCGNO73 \
  | 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: 22d9d5371bb16eebc28e9e46e119aefefc6db168dd6fa243175392465d7b33b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4297173683f0e539f32c7c5fa147590f9fb188e9c381afa16e62857acea387a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-08-03T08:30:14Z",
    "title_canon_sha256": "cfb69b5f411add51c820e9b13e9d9358370676370b00444d60257fdeeeb1291b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.01889",
    "kind": "arxiv",
    "version": 1
  }
}