Pith Number

pith:M4RTCRGS

pith:2026:M4RTCRGSYPEPBTAJBJAA236DIG

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Clearing in Liability Networks via Sheaves on Directed Hypergraphs

Robert Ghrist

Liability clearing configurations are precisely the global sections of a sheaf on a directed hypergraph.

arxiv:2605.15778 v1 · 2026-05-15 · q-fin.MF · math.CT

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Claims

C1strongest claim

Clearing configurations are precisely the global sections of this sheaf, and the global-section object is canonically the equalizer of the identity and a clearing operator Φ=A∘D factored into collective distribution D and aggregation A; an institution-edge duality identifies it equivalently with the equalizer of the dual operator D∘A on the edge side. This identifies liability clearing as a finite-limit construction in the ambient data category.

C2weakest assumption

That a decorated liability network can be represented as a directed hypergraph whose hyperedges separate payment distribution from receipt collection, and that the coefficient category admits finite limits together with constraint subobjects compatible with a finite-limit-preserving functor.

C3one line summary

Liability clearing in networks is modeled as global sections of a liability sheaf on directed hypergraphs, identified as a finite-limit construction with existence and uniqueness from lattice and metric theorems on payment objects.

References

33 extracted · 33 resolved · 1 Pith anchors

[1] Daron Acemoglu, Asuman Ozdaglar, and Alireza Tahbaz-Salehi,Systemic risk and stability in financial networks, American Economic Review105(2015), no. 2, 564–608 2015

[2] Kartik Anand, Ben Craig, and Goetz von Peter,Filling in the blanks: Network structure and interbank contagion, Quantitative Finance15(2015), no. 4, 625–636 2015

[3] 2025 Sheaf theory: from deep geometry to deep learning 2025

[4] Tathagata Banerjee, Alex Bernstein, and Zachary Feinstein,Dynamic clearing and contagion in finan- cial networks, EuropeanJournalofOperationalResearch321(2025), no.2, 664–675, arXiv:1801.02091 2025

[5] Tathagata Banerjee and Zachary Feinstein,Impact of contingent payments on systemic risk in financial networks, Mathematics and Financial Economics13(2019), no. 4, 617–636 2019

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:17.843836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67233144d2c3c8f0cc090a400d6fc341b1a40826774009eb318d304c09b18e0c

Aliases

arxiv: 2605.15778 · arxiv_version: 2605.15778v1 · doi: 10.48550/arxiv.2605.15778 · pith_short_12: M4RTCRGSYPEP · pith_short_16: M4RTCRGSYPEPBTAJ · pith_short_8: M4RTCRGS

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/M4RTCRGSYPEPBTAJBJAA236DIG \
  | 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: 67233144d2c3c8f0cc090a400d6fc341b1a40826774009eb318d304c09b18e0c

Canonical record JSON

{
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      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-fin.MF",
    "submitted_at": "2026-05-15T09:36:25Z",
    "title_canon_sha256": "ec9530d7b19daae79cbf90f806608d3be969ae10863b15c67e0784c42f417d0a"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}