{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:F3N7X36GHSMXWLUQ5UMMAYKWYI","short_pith_number":"pith:F3N7X36G","canonical_record":{"source":{"id":"1411.0944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-11-04T15:43:18Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"8354c631b391b43bb0f765d2c85325dddd4f70c8263456b07013c0d2ae861ec1","abstract_canon_sha256":"c3f1806a02eaf7fabf5eea212024e8d5190b7f80bcbf451d120dc3703d5a56db"},"schema_version":"1.0"},"canonical_sha256":"2edbfbefc63c997b2e90ed18c06156c21743061dd50302f9d56a7ac9113e13c4","source":{"kind":"arxiv","id":"1411.0944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0944","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0944v1","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0944","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"F3N7X36GHSMX","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3N7X36GHSMXWLUQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3N7X36G","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:F3N7X36GHSMXWLUQ5UMMAYKWYI","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-11-04T15:43:18Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"8354c631b391b43bb0f765d2c85325dddd4f70c8263456b07013c0d2ae861ec1","abstract_canon_sha256":"c3f1806a02eaf7fabf5eea212024e8d5190b7f80bcbf451d120dc3703d5a56db"},"schema_version":"1.0"},"canonical_sha256":"2edbfbefc63c997b2e90ed18c06156c21743061dd50302f9d56a7ac9113e13c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:03.323527Z","signature_b64":"8+e6yq07RsHYs66j2DtcCSHeqZFMCxeGxx7Zp3uGZsyHsL4wrixT5ZHrevtCz5OQqNLYoYC9QXXuRXiVkJSJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2edbfbefc63c997b2e90ed18c06156c21743061dd50302f9d56a7ac9113e13c4","last_reissued_at":"2026-05-18T01:22:03.323086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:03.323086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0944","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r84yUPaoaorvzsS0xZOBFgbQMNwJCB0PCkH2CsX3+29tpez96exlNaTLACqaflSUQh3wKzE6jnvMXgm3Go/6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:22:48.911972Z"},"content_sha256":"c5561e059987d5b65e436f7a22a0eb38d3bd1ec3cd834f9bfdc5102d55b425e0","schema_version":"1.0","event_id":"sha256:c5561e059987d5b65e436f7a22a0eb38d3bd1ec3cd834f9bfdc5102d55b425e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:F3N7X36GHSMXWLUQ5UMMAYKWYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The cost of getting local monotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.GT","authors_text":"Josep Freixas, Sascha Kurz","submitted_at":"2014-11-04T15:43:18Z","abstract_excerpt":"Manfred Holler introduced the Public Good index as a proposal to divide a public good among players. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback or as an advantage."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0944","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbXadn9WAx51JEQnJW7NMd4NG0hBGNr4LQx0xuLHppiccywNaZAe7FcLQR0DYIbX1kf+nar00MUQrB5+fCKfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:22:48.912654Z"},"content_sha256":"5f17f7c7b4619b6b33d87bdd96864247a305c6a950e1dc4e52110b4ec7ac9486","schema_version":"1.0","event_id":"sha256:5f17f7c7b4619b6b33d87bdd96864247a305c6a950e1dc4e52110b4ec7ac9486"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3N7X36GHSMXWLUQ5UMMAYKWYI/bundle.json","state_url":"https://pith.science/pith/F3N7X36GHSMXWLUQ5UMMAYKWYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3N7X36GHSMXWLUQ5UMMAYKWYI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T01:22:48Z","links":{"resolver":"https://pith.science/pith/F3N7X36GHSMXWLUQ5UMMAYKWYI","bundle":"https://pith.science/pith/F3N7X36GHSMXWLUQ5UMMAYKWYI/bundle.json","state":"https://pith.science/pith/F3N7X36GHSMXWLUQ5UMMAYKWYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3N7X36GHSMXWLUQ5UMMAYKWYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F3N7X36GHSMXWLUQ5UMMAYKWYI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c3f1806a02eaf7fabf5eea212024e8d5190b7f80bcbf451d120dc3703d5a56db","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-11-04T15:43:18Z","title_canon_sha256":"8354c631b391b43bb0f765d2c85325dddd4f70c8263456b07013c0d2ae861ec1"},"schema_version":"1.0","source":{"id":"1411.0944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0944","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0944v1","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0944","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"F3N7X36GHSMX","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3N7X36GHSMXWLUQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3N7X36G","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:5f17f7c7b4619b6b33d87bdd96864247a305c6a950e1dc4e52110b4ec7ac9486","target":"graph","created_at":"2026-05-18T01:22:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Manfred Holler introduced the Public Good index as a proposal to divide a public good among players. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback or as an advantage.","authors_text":"Josep Freixas, Sascha Kurz","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-11-04T15:43:18Z","title":"The cost of getting local monotonicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0944","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c5561e059987d5b65e436f7a22a0eb38d3bd1ec3cd834f9bfdc5102d55b425e0","target":"record","created_at":"2026-05-18T01:22:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c3f1806a02eaf7fabf5eea212024e8d5190b7f80bcbf451d120dc3703d5a56db","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-11-04T15:43:18Z","title_canon_sha256":"8354c631b391b43bb0f765d2c85325dddd4f70c8263456b07013c0d2ae861ec1"},"schema_version":"1.0","source":{"id":"1411.0944","kind":"arxiv","version":1}},"canonical_sha256":"2edbfbefc63c997b2e90ed18c06156c21743061dd50302f9d56a7ac9113e13c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2edbfbefc63c997b2e90ed18c06156c21743061dd50302f9d56a7ac9113e13c4","first_computed_at":"2026-05-18T01:22:03.323086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:03.323086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+e6yq07RsHYs66j2DtcCSHeqZFMCxeGxx7Zp3uGZsyHsL4wrixT5ZHrevtCz5OQqNLYoYC9QXXuRXiVkJSJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:03.323527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5561e059987d5b65e436f7a22a0eb38d3bd1ec3cd834f9bfdc5102d55b425e0","sha256:5f17f7c7b4619b6b33d87bdd96864247a305c6a950e1dc4e52110b4ec7ac9486"],"state_sha256":"59847bf61e6ec200fd6d78ecfc778c9ea6ca46a3b5eaec81307c1118a15f85f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKH97CsFULOL1awF2uiDjnU5UDHWpLY6oakVezlysOSKA5/zhnTo2/lCuVe4o1eHxTDAiTVdAhVJlcFcWGFVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:22:48.916040Z","bundle_sha256":"c4ed837b4462412ad3d5f1effc05e123609d46c7f4ac3be26f2a94ac265babad"}}