Pith Number

pith:VPIQHMKE

pith:2026:VPIQHMKE7Y7Q7YTW53AC2ZYF42

not attested not anchored not stored refs pending

A Nash Equilibrium Framework For Training-Free Multimodal Step Verification

Amit Sharma, Kunal Tilaganji, Nagarajan Natarajan, Rohit Sinha, Tanuja Ganu, Vineeth N. Balasubramanian

arxiv:2605.20033 v1 · 2026-05-19 · cs.CV · 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{VPIQHMKE7Y7Q7YTW53AC2ZYF42}

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	2026-05-20T02:05:59.644090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd103b144fe3f0fe276eec02d6705e6ad431bbb4bc9214cf1407ec8be80e15c

Aliases

arxiv: 2605.20033 · arxiv_version: 2605.20033v1 · doi: 10.48550/arxiv.2605.20033 · pith_short_12: VPIQHMKE7Y7Q · pith_short_16: VPIQHMKE7Y7Q7YTW · pith_short_8: VPIQHMKE

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/VPIQHMKE7Y7Q7YTW53AC2ZYF42 \
  | 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: abd103b144fe3f0fe276eec02d6705e6ad431bbb4bc9214cf1407ec8be80e15c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "268b3761b513563717574d061e43ffc1bd69c0a11923ab1825154b2107715828",
    "cross_cats_sorted": [
      "cs.GT"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.CV",
    "submitted_at": "2026-05-19T15:54:22Z",
    "title_canon_sha256": "6dfa8a728e1e89b4a93c7128d55ab0289effd7bf62edbcc00e68d2ff6fe31f6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20033",
    "kind": "arxiv",
    "version": 1
  }
}