{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Z3LF53UFZCSKYHZDYDYF4YSV5K","short_pith_number":"pith:Z3LF53UF","canonical_record":{"source":{"id":"1608.06797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-24T12:50:52Z","cross_cats_sorted":[],"title_canon_sha256":"c59486d387b76e3fd64a616a577224da11f831b0b82782c12728a50f2e42d651","abstract_canon_sha256":"cc85f0e77f0f1283150be67f27fd8921ae38edb2bcc899d954e3aecd82c9749f"},"schema_version":"1.0"},"canonical_sha256":"ced65eee85c8a4ac1f23c0f05e6255eabf6eb767d1c3d859f6a7dc41ac6b2c18","source":{"kind":"arxiv","id":"1608.06797","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06797","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06797v1","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06797","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"Z3LF53UFZCSK","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z3LF53UFZCSKYHZD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z3LF53UF","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Z3LF53UFZCSKYHZDYDYF4YSV5K","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-24T12:50:52Z","cross_cats_sorted":[],"title_canon_sha256":"c59486d387b76e3fd64a616a577224da11f831b0b82782c12728a50f2e42d651","abstract_canon_sha256":"cc85f0e77f0f1283150be67f27fd8921ae38edb2bcc899d954e3aecd82c9749f"},"schema_version":"1.0"},"canonical_sha256":"ced65eee85c8a4ac1f23c0f05e6255eabf6eb767d1c3d859f6a7dc41ac6b2c18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:57.486717Z","signature_b64":"Qm3UvqRtpztRUkzLdK2jcXlOYLAQvtp6IfZxoOGyJMOcGxst6Vjlk4HQGBUe6uuAMPA4DQExT0Y/sWBYhzNcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ced65eee85c8a4ac1f23c0f05e6255eabf6eb767d1c3d859f6a7dc41ac6b2c18","last_reissued_at":"2026-05-18T01:07:57.486235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:57.486235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06797","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":"2026-05-18T01:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jh2laaQOVTbTfkWCCyKlB74chGIz5VLuAM/jJ+4zHLv66eMbhs2qtVQsYprlX3VFFe05thZ1kIDGvuSFCcEVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:25:39.430997Z"},"content_sha256":"4834c7c88912b03688d1810026781e206436a227888e9f49247bc2d480df3ca3","schema_version":"1.0","event_id":"sha256:4834c7c88912b03688d1810026781e206436a227888e9f49247bc2d480df3ca3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Z3LF53UFZCSKYHZDYDYF4YSV5K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Additive Stabilizers for Unstable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Andreas Wierz, Britta Peis, Corinna Gottschalk, Daniel Schmand, Jochen K\\\"onemann, Karthekeyan Chandrasekaran","submitted_at":"2016-08-24T12:50:52Z","abstract_excerpt":"Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a network bargaining game with a balanced solution. A graph with weighted edges is called stable if the maximum weight of an integral matching equals the cost of a minimum fractional weighted vertex cover. If a graph is not stable, it can be stabilized in different ways. Recent papers have considered the deletion or addition of edges and vertices in order to stabil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06797","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":"2026-05-18T01:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQfYm4VLlZZ/2N2QfSTcSxxt902mtjfa7B1/PmszxICWyzjnoZNQ4qmQkMCXAGRmLHWxzcdXqyhzKVnwg8ZbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:25:39.431392Z"},"content_sha256":"3323e3da412df093a737ced0a5f58ae60d5848737c21d4d0ee6acf265a82c9b4","schema_version":"1.0","event_id":"sha256:3323e3da412df093a737ced0a5f58ae60d5848737c21d4d0ee6acf265a82c9b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3LF53UFZCSKYHZDYDYF4YSV5K/bundle.json","state_url":"https://pith.science/pith/Z3LF53UFZCSKYHZDYDYF4YSV5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3LF53UFZCSKYHZDYDYF4YSV5K/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":"2026-05-28T21:25:39Z","links":{"resolver":"https://pith.science/pith/Z3LF53UFZCSKYHZDYDYF4YSV5K","bundle":"https://pith.science/pith/Z3LF53UFZCSKYHZDYDYF4YSV5K/bundle.json","state":"https://pith.science/pith/Z3LF53UFZCSKYHZDYDYF4YSV5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3LF53UFZCSKYHZDYDYF4YSV5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z3LF53UFZCSKYHZDYDYF4YSV5K","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":"cc85f0e77f0f1283150be67f27fd8921ae38edb2bcc899d954e3aecd82c9749f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-24T12:50:52Z","title_canon_sha256":"c59486d387b76e3fd64a616a577224da11f831b0b82782c12728a50f2e42d651"},"schema_version":"1.0","source":{"id":"1608.06797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06797","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06797v1","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06797","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"Z3LF53UFZCSK","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z3LF53UFZCSKYHZD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z3LF53UF","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:3323e3da412df093a737ced0a5f58ae60d5848737c21d4d0ee6acf265a82c9b4","target":"graph","created_at":"2026-05-18T01:07:57Z","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":"Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a network bargaining game with a balanced solution. A graph with weighted edges is called stable if the maximum weight of an integral matching equals the cost of a minimum fractional weighted vertex cover. If a graph is not stable, it can be stabilized in different ways. Recent papers have considered the deletion or addition of edges and vertices in order to stabil","authors_text":"Andreas Wierz, Britta Peis, Corinna Gottschalk, Daniel Schmand, Jochen K\\\"onemann, Karthekeyan Chandrasekaran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-24T12:50:52Z","title":"Additive Stabilizers for Unstable Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06797","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":"sha256:4834c7c88912b03688d1810026781e206436a227888e9f49247bc2d480df3ca3","target":"record","created_at":"2026-05-18T01:07:57Z","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":"cc85f0e77f0f1283150be67f27fd8921ae38edb2bcc899d954e3aecd82c9749f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-24T12:50:52Z","title_canon_sha256":"c59486d387b76e3fd64a616a577224da11f831b0b82782c12728a50f2e42d651"},"schema_version":"1.0","source":{"id":"1608.06797","kind":"arxiv","version":1}},"canonical_sha256":"ced65eee85c8a4ac1f23c0f05e6255eabf6eb767d1c3d859f6a7dc41ac6b2c18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ced65eee85c8a4ac1f23c0f05e6255eabf6eb767d1c3d859f6a7dc41ac6b2c18","first_computed_at":"2026-05-18T01:07:57.486235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:57.486235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qm3UvqRtpztRUkzLdK2jcXlOYLAQvtp6IfZxoOGyJMOcGxst6Vjlk4HQGBUe6uuAMPA4DQExT0Y/sWBYhzNcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:57.486717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4834c7c88912b03688d1810026781e206436a227888e9f49247bc2d480df3ca3","sha256:3323e3da412df093a737ced0a5f58ae60d5848737c21d4d0ee6acf265a82c9b4"],"state_sha256":"5dad3eb83440df3ff250c09e3a1ef9bb84938b66408c8472f17e6eb6a798316e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWb2/npBwWfh65W1Iga1ZdU1GfcHRLA6sUUPLXtBr4PoFPw8+e8LmnlXLZ1XVjNKK6ySRpXwa/cnQt7B0Sc+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:25:39.434748Z","bundle_sha256":"8d76b98eed92fa7b0c7373c5b54d5bb550918a33be1e3592f50d3a738d9bc0f0"}}