Pith Number

pith:QCS66UIR

pith:2025:QCS66UIRWAQG7P2D4KWT374SFL

not attested not anchored not stored refs pending

A Mean Field Game for Capacity Expansion Modeling

Dimitrios Lolas, Emma Hubert, Ronnie Sircar

arxiv:2507.10604 v1 · 2025-07-12 · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QCS66UIRWAQG7P2D4KWT374SFL}

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.

Cited by

1 paper in Pith

Modeling Stochastic Multi-Agent Interaction in Intraday Battery Energy Storage Dispatch with Market Power

Receipt and verification

First computed	2026-07-05T11:36:57.357378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80a5ef5111b0206fbf43e2ad3dff922acc0b5f84eb346984726a97d05636506d

Aliases

arxiv: 2507.10604 · arxiv_version: 2507.10604v1 · doi: 10.48550/arxiv.2507.10604 · pith_short_12: QCS66UIRWAQG · pith_short_16: QCS66UIRWAQG7P2D · pith_short_8: QCS66UIR

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/QCS66UIRWAQG7P2D4KWT374SFL \
  | 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: 80a5ef5111b0206fbf43e2ad3dff922acc0b5f84eb346984726a97d05636506d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98104546aff03af7c17d43761a56df9947b99ea054379bcf03bd90a0d76b1575",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-07-12T21:38:21Z",
    "title_canon_sha256": "00a39d17ba52cb74e183bf42d3ea2b11469b2bf0f8602e5819c7a05e07c8cd99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.10604",
    "kind": "arxiv",
    "version": 1
  }
}