{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:THXGV3EKOTV6WGM4JDQQRPPRT2","short_pith_number":"pith:THXGV3EK","canonical_record":{"source":{"id":"1707.02760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-10T09:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"9e71f249e84fdd7b0c5103b4b55f22bc95169056b7aa5c60d999867a82af0d3c","abstract_canon_sha256":"788fbfe0f2a2f4297f82b8fc01db88f8e9153b8d0fdcf30bc8a0ad00fc5dd92c"},"schema_version":"1.0"},"canonical_sha256":"99ee6aec8a74ebeb199c48e108bdf19e8319aea4ee4c93064304351cf7915fdd","source":{"kind":"arxiv","id":"1707.02760","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02760","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02760v1","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02760","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"pith_short_12","alias_value":"THXGV3EKOTV6","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"THXGV3EKOTV6WGM4","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"THXGV3EK","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:THXGV3EKOTV6WGM4JDQQRPPRT2","target":"record","payload":{"canonical_record":{"source":{"id":"1707.02760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-10T09:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"9e71f249e84fdd7b0c5103b4b55f22bc95169056b7aa5c60d999867a82af0d3c","abstract_canon_sha256":"788fbfe0f2a2f4297f82b8fc01db88f8e9153b8d0fdcf30bc8a0ad00fc5dd92c"},"schema_version":"1.0"},"canonical_sha256":"99ee6aec8a74ebeb199c48e108bdf19e8319aea4ee4c93064304351cf7915fdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:35.839294Z","signature_b64":"xNb4DtToV3ufg3UNKyrRP/LC5bI+rjk9b0nngJnYmgFD29RJwICPxsED9oIS7VbHoWNV+zxnZ1rHixweTdGhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99ee6aec8a74ebeb199c48e108bdf19e8319aea4ee4c93064304351cf7915fdd","last_reissued_at":"2026-05-18T00:40:35.838599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:35.838599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.02760","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":"2026-05-18T00:40:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xRcl/WKm7y6Ka1oepwIDMXeVgYn2g9/MJ5P0EvAqYZjVfKr6oetgU8/BL6/m/HXWXQa7JTT6ckDbSzb5zyN0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:37:24.482342Z"},"content_sha256":"1c34f4021d0b15b4aab2a1c73e3f778057c76a6493eac156859d277209aa54b6","schema_version":"1.0","event_id":"sha256:1c34f4021d0b15b4aab2a1c73e3f778057c76a6493eac156859d277209aa54b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:THXGV3EKOTV6WGM4JDQQRPPRT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Power domination on triangular grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Claire Pennarun (LaBRI), Prosenjit Bose, Sander Verdonschot","submitted_at":"2017-07-10T09:06:58Z","abstract_excerpt":"The concept of power domination emerged from the problem of monitoring electrical systems. Given a graph G and a set S $\\subseteq$ V (G), a set M of monitored vertices is built as follows: at first, M contains only the vertices of S and their direct neighbors, and then each time a vertex in M has exactly one neighbor not in M, this neighbor is added to M. The power domination number of a graph G is the minimum size of a set S such that this process ends up with the set M containing every vertex of G. We here show that the power domination number of a triangular grid T\\_k with hexagonal-shape b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02760","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":"2026-05-18T00:40:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUOvEBMGsQ2qTrp5vmKJ+WFJwwv9M3GJXPRmYnrNABl3g772VT56NibVWNyEEOUzRh7FFPlJ3zD97CGE6J0EBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:37:24.482721Z"},"content_sha256":"51ae640a9ec6c8f4614b0a72ef1f085a5ecd5549b59bd5cf3c4c080932eb0bfe","schema_version":"1.0","event_id":"sha256:51ae640a9ec6c8f4614b0a72ef1f085a5ecd5549b59bd5cf3c4c080932eb0bfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THXGV3EKOTV6WGM4JDQQRPPRT2/bundle.json","state_url":"https://pith.science/pith/THXGV3EKOTV6WGM4JDQQRPPRT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THXGV3EKOTV6WGM4JDQQRPPRT2/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":"2026-05-25T19:37:24Z","links":{"resolver":"https://pith.science/pith/THXGV3EKOTV6WGM4JDQQRPPRT2","bundle":"https://pith.science/pith/THXGV3EKOTV6WGM4JDQQRPPRT2/bundle.json","state":"https://pith.science/pith/THXGV3EKOTV6WGM4JDQQRPPRT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THXGV3EKOTV6WGM4JDQQRPPRT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:THXGV3EKOTV6WGM4JDQQRPPRT2","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":"788fbfe0f2a2f4297f82b8fc01db88f8e9153b8d0fdcf30bc8a0ad00fc5dd92c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-10T09:06:58Z","title_canon_sha256":"9e71f249e84fdd7b0c5103b4b55f22bc95169056b7aa5c60d999867a82af0d3c"},"schema_version":"1.0","source":{"id":"1707.02760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02760","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02760v1","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02760","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"pith_short_12","alias_value":"THXGV3EKOTV6","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"THXGV3EKOTV6WGM4","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"THXGV3EK","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:51ae640a9ec6c8f4614b0a72ef1f085a5ecd5549b59bd5cf3c4c080932eb0bfe","target":"graph","created_at":"2026-05-18T00:40:35Z","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":"The concept of power domination emerged from the problem of monitoring electrical systems. Given a graph G and a set S $\\subseteq$ V (G), a set M of monitored vertices is built as follows: at first, M contains only the vertices of S and their direct neighbors, and then each time a vertex in M has exactly one neighbor not in M, this neighbor is added to M. The power domination number of a graph G is the minimum size of a set S such that this process ends up with the set M containing every vertex of G. We here show that the power domination number of a triangular grid T\\_k with hexagonal-shape b","authors_text":"Claire Pennarun (LaBRI), Prosenjit Bose, Sander Verdonschot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-10T09:06:58Z","title":"Power domination on triangular grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02760","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":"sha256:1c34f4021d0b15b4aab2a1c73e3f778057c76a6493eac156859d277209aa54b6","target":"record","created_at":"2026-05-18T00:40:35Z","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":"788fbfe0f2a2f4297f82b8fc01db88f8e9153b8d0fdcf30bc8a0ad00fc5dd92c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-10T09:06:58Z","title_canon_sha256":"9e71f249e84fdd7b0c5103b4b55f22bc95169056b7aa5c60d999867a82af0d3c"},"schema_version":"1.0","source":{"id":"1707.02760","kind":"arxiv","version":1}},"canonical_sha256":"99ee6aec8a74ebeb199c48e108bdf19e8319aea4ee4c93064304351cf7915fdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99ee6aec8a74ebeb199c48e108bdf19e8319aea4ee4c93064304351cf7915fdd","first_computed_at":"2026-05-18T00:40:35.838599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:35.838599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xNb4DtToV3ufg3UNKyrRP/LC5bI+rjk9b0nngJnYmgFD29RJwICPxsED9oIS7VbHoWNV+zxnZ1rHixweTdGhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:35.839294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c34f4021d0b15b4aab2a1c73e3f778057c76a6493eac156859d277209aa54b6","sha256:51ae640a9ec6c8f4614b0a72ef1f085a5ecd5549b59bd5cf3c4c080932eb0bfe"],"state_sha256":"f9e41330247974ef29b70cd23daf6c74d12488a210cc3217b0278de9e65af6ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zZOA4cz4BOaOn5QIkf82lrcPvInUgazovA4ytl12Pekg1iN5xVeowmXYkkgV6RmWqJqJRZbb1ig1kvHMQUHCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:37:24.485518Z","bundle_sha256":"7891991ca85b82d68bc8d35cd6e01037789322ea9db6d4312eddeab1c5756cae"}}