Pith Number

pith:4IICSKIT

pith:2026:4IICSKIT54VNRAXNXITDA2JG5U

not attested not anchored not stored refs pending

Invariant Price of Anarchy and Multiplicative Smoothness

Heinrich H. Nax, Ilia Shilov, Saverio Bolognani

arxiv:2606.11397 v1 · 2026-06-09 · cs.GT · econ.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4IICSKIT54VNRAXNXITDA2JG5U}

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	2026-06-11T00:08:23.552995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e210292913ef2ad882edba26306926ed26858c8a7d236ad9f2a8c7c4bd47e3f4

Aliases

arxiv: 2606.11397 · arxiv_version: 2606.11397v1 · doi: 10.48550/arxiv.2606.11397 · pith_short_12: 4IICSKIT54VN · pith_short_16: 4IICSKIT54VNRAXN · pith_short_8: 4IICSKIT

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/4IICSKIT54VNRAXNXITDA2JG5U \
  | 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: e210292913ef2ad882edba26306926ed26858c8a7d236ad9f2a8c7c4bd47e3f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37a2ae0222d16a3780e32af68fdd2eb6310351f7ca800b493e43f69ff11adfdb",
    "cross_cats_sorted": [
      "econ.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-06-09T19:36:56Z",
    "title_canon_sha256": "0cb16e1d3db66dd8c72d9271f7389f4bf12964d1a3cf1d09248ccdafe019ecf6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11397",
    "kind": "arxiv",
    "version": 1
  }
}