Pith Number

pith:Z2YBKC2N

pith:2026:Z2YBKC2NLDQFJDF4ZZS6ZU66K3

not attested not anchored not stored refs pending

Stable Matchings with Choice Correspondences Under Acyclicity

Mihir Bhattacharya, Ojasvi Khare, Varun Bansal

Stable matchings exist in many-to-many markets when choice correspondences are substitutable and generally acyclic.

arxiv:2603.23038 v5 · 2026-03-24 · 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{Z2YBKC2NLDQFJDF4ZZS6ZU66K3}

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.

Claims

C1strongest claim

We show that stable matchings exist when choice correspondences satisfy substitutability and a new general acyclicity condition. We provide a constructive proof using a Grow or Discard Algorithm that iteratively expands or eliminates contracts until a strongly maximal individually rational set is reached.

C2weakest assumption

Choice correspondences satisfy substitutability together with the newly introduced general acyclicity condition (weaker than path independence) for the many-to-many case.

C3one line summary

Stable matchings exist under substitutability and general acyclicity for choice correspondences in many-to-many markets, constructed via a Grow or Discard algorithm that avoids permanent rejection of contracts.

Receipt and verification

First computed	2026-05-20T02:05:42.381986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceb0150b4d58e0548cbcce65ecd3de56d784f62b70391275faa1f731066ba54d

Aliases

arxiv: 2603.23038 · arxiv_version: 2603.23038v5 · doi: 10.48550/arxiv.2603.23038 · pith_short_12: Z2YBKC2NLDQF · pith_short_16: Z2YBKC2NLDQFJDF4 · pith_short_8: Z2YBKC2N

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/Z2YBKC2NLDQFJDF4ZZS6ZU66K3 \
  | 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: ceb0150b4d58e0548cbcce65ecd3de56d784f62b70391275faa1f731066ba54d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eac940dd2983a640bbda616900250847432bcfee23f9c8fab29e2d1bf23c336d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "econ.TH",
    "submitted_at": "2026-03-24T10:18:07Z",
    "title_canon_sha256": "98e9e6c19fbe8501e9a065d2be60d155f32ec654adf532d367efbb1091824071"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.23038",
    "kind": "arxiv",
    "version": 5
  }
}