Pith Number

pith:O2UPFVMG

pith:2016:O2UPFVMG6APA6YTHKHLGT67IGX

not attested not anchored not stored refs pending

Primal-Dual Method for Searching Equilibrium in Hierarchical Congestion Population Games

Alexander Gasnikov, Anton Rodomanov, Evgenia Gasnikova, Inna Usik, Pavel Dvurechensky, Sergey Matsievsky

arxiv:1606.08988 v2 · 2016-06-29 · 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{O2UPFVMG6APA6YTHKHLGT67IGX}

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	2026-05-18T01:07:56.543788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76a8f2d586f01e0f626751d669fbe835f10c154cb634fc2b6eecfa7a9cf88791

Aliases

arxiv: 1606.08988 · arxiv_version: 1606.08988v2 · doi: 10.48550/arxiv.1606.08988 · pith_short_12: O2UPFVMG6APA · pith_short_16: O2UPFVMG6APA6YTH · pith_short_8: O2UPFVMG

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/O2UPFVMG6APA6YTHKHLGT67IGX \
  | 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: 76a8f2d586f01e0f626751d669fbe835f10c154cb634fc2b6eecfa7a9cf88791

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d8c635f03abe34db687156aaf0f06b88d3c89ff194590007000c50a0c2596e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-06-29T07:49:09Z",
    "title_canon_sha256": "055e3b591c77c8fd9032368ec9921c8576e25c21f9a9d43c13ad2f230d8f6b7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08988",
    "kind": "arxiv",
    "version": 2
  }
}