Pith Number

pith:N4P6WKIR

pith:2026:N4P6WKIRR44FRCRJAXJTOJB5XH

not attested not anchored not stored refs pending

Phase Transitions in Turnpike Theory For Mean-Field Games

Siddharth Karuturi

arxiv:2605.20213 v1 · 2026-04-24 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N4P6WKIRR44FRCRJAXJTOJB5XH}

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	2026-05-21T00:04:21.330743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f1feb29118f38588a2905d337243db9ff98faea8162e904abbde9658229431f

Aliases

arxiv: 2605.20213 · arxiv_version: 2605.20213v1 · doi: 10.48550/arxiv.2605.20213 · pith_short_12: N4P6WKIRR44F · pith_short_16: N4P6WKIRR44FRCRJ · pith_short_8: N4P6WKIR

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/N4P6WKIRR44FRCRJAXJTOJB5XH \
  | 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: 6f1feb29118f38588a2905d337243db9ff98faea8162e904abbde9658229431f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5dd63c86020031d0fc38a79d544f5adad27b823665418c1bdfec1709f45baae",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-04-24T23:10:34Z",
    "title_canon_sha256": "6c1633c633ee6b3c91179f16841f6a4e1627785c7d4c2996e1a1432ac4f7c13b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20213",
    "kind": "arxiv",
    "version": 1
  }
}