{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:PIER6XCFHSGJTS3O5EWWSVVB6A","short_pith_number":"pith:PIER6XCF","canonical_record":{"source":{"id":"2206.13182","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-27T10:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"ef070b36bedfac2d6db3a05398d64493ddbf3d5a4f100d57561bf9789a19bd19","abstract_canon_sha256":"daf2c0f7b1d2a46522bde5b14c4c00aaa7903560dd8fa49ceabae824af26ef39"},"schema_version":"1.0"},"canonical_sha256":"7a091f5c453c8c99cb6ee92d6956a1f00c701aa832095b27048009b2ece9095b","source":{"kind":"arxiv","id":"2206.13182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.13182","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"2206.13182v1","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.13182","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"PIER6XCFHSGJ","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_16","alias_value":"PIER6XCFHSGJTS3O","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_8","alias_value":"PIER6XCF","created_at":"2026-07-05T08:54:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:PIER6XCFHSGJTS3O5EWWSVVB6A","target":"record","payload":{"canonical_record":{"source":{"id":"2206.13182","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-27T10:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"ef070b36bedfac2d6db3a05398d64493ddbf3d5a4f100d57561bf9789a19bd19","abstract_canon_sha256":"daf2c0f7b1d2a46522bde5b14c4c00aaa7903560dd8fa49ceabae824af26ef39"},"schema_version":"1.0"},"canonical_sha256":"7a091f5c453c8c99cb6ee92d6956a1f00c701aa832095b27048009b2ece9095b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:54:00.248722Z","signature_b64":"TUrxQpDcl1ehLUJgSbkglVtk7tUE+Xh56126V6+fU5R2tCnIOx8ol80oDgA6f/MiSgPD7Czr9FYU9CvBVkeQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a091f5c453c8c99cb6ee92d6956a1f00c701aa832095b27048009b2ece9095b","last_reissued_at":"2026-07-05T08:54:00.248216Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:54:00.248216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.13182","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":"2026-07-05T08:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eC4Tc0Rk7YCmONzfUwurMt5quplvdgeSWOdlCNyGb5uyXJsJO2WXJfzTllzzXkAaYbp++abGPNHo20aDDpBACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T06:18:54.398731Z"},"content_sha256":"16f9c5e1da3e0169be7180ef2d97f8a0bf195d006c3f3d73203ad126839d3d14","schema_version":"1.0","event_id":"sha256:16f9c5e1da3e0169be7180ef2d97f8a0bf195d006c3f3d73203ad126839d3d14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:PIER6XCFHSGJTS3O5EWWSVVB6A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the number of minimum dominating sets and total dominating sets in forests","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Petr, Julien Portier, Leo Versteegen","submitted_at":"2022-06-27T10:54:04Z","abstract_excerpt":"We show that the maximum number of minimum dominating sets of a forest with domination number $\\gamma$ is at most $\\sqrt{5}^{\\gamma}$ and construct for each $\\gamma$ a tree with domination number $\\gamma$ that has more than $\\frac{2}{5}\\sqrt{5}^{\\gamma}$ minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.13182","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.13182/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lT0DQQWiQf9c4WHLCG3mnCxS7nzvYmzPTfERqhy+lnVBNptltj97XNJbbnR2KUWjMvYgGWzVBLZNAsPWDyTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T06:18:54.399106Z"},"content_sha256":"78a3d1711f116bb2e440315e6362cd4a8be2f169f932944a422e1a789cae5f44","schema_version":"1.0","event_id":"sha256:78a3d1711f116bb2e440315e6362cd4a8be2f169f932944a422e1a789cae5f44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PIER6XCFHSGJTS3O5EWWSVVB6A/bundle.json","state_url":"https://pith.science/pith/PIER6XCFHSGJTS3O5EWWSVVB6A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PIER6XCFHSGJTS3O5EWWSVVB6A/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":"2026-07-09T06:18:54Z","links":{"resolver":"https://pith.science/pith/PIER6XCFHSGJTS3O5EWWSVVB6A","bundle":"https://pith.science/pith/PIER6XCFHSGJTS3O5EWWSVVB6A/bundle.json","state":"https://pith.science/pith/PIER6XCFHSGJTS3O5EWWSVVB6A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PIER6XCFHSGJTS3O5EWWSVVB6A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PIER6XCFHSGJTS3O5EWWSVVB6A","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":"daf2c0f7b1d2a46522bde5b14c4c00aaa7903560dd8fa49ceabae824af26ef39","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-27T10:54:04Z","title_canon_sha256":"ef070b36bedfac2d6db3a05398d64493ddbf3d5a4f100d57561bf9789a19bd19"},"schema_version":"1.0","source":{"id":"2206.13182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.13182","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"2206.13182v1","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.13182","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"PIER6XCFHSGJ","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_16","alias_value":"PIER6XCFHSGJTS3O","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_8","alias_value":"PIER6XCF","created_at":"2026-07-05T08:54:00Z"}],"graph_snapshots":[{"event_id":"sha256:78a3d1711f116bb2e440315e6362cd4a8be2f169f932944a422e1a789cae5f44","target":"graph","created_at":"2026-07-05T08:54:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.13182/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the maximum number of minimum dominating sets of a forest with domination number $\\gamma$ is at most $\\sqrt{5}^{\\gamma}$ and construct for each $\\gamma$ a tree with domination number $\\gamma$ that has more than $\\frac{2}{5}\\sqrt{5}^{\\gamma}$ minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach.","authors_text":"Jan Petr, Julien Portier, Leo Versteegen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-27T10:54:04Z","title":"On the number of minimum dominating sets and total dominating sets in forests"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.13182","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":"sha256:16f9c5e1da3e0169be7180ef2d97f8a0bf195d006c3f3d73203ad126839d3d14","target":"record","created_at":"2026-07-05T08:54:00Z","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":"daf2c0f7b1d2a46522bde5b14c4c00aaa7903560dd8fa49ceabae824af26ef39","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-27T10:54:04Z","title_canon_sha256":"ef070b36bedfac2d6db3a05398d64493ddbf3d5a4f100d57561bf9789a19bd19"},"schema_version":"1.0","source":{"id":"2206.13182","kind":"arxiv","version":1}},"canonical_sha256":"7a091f5c453c8c99cb6ee92d6956a1f00c701aa832095b27048009b2ece9095b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a091f5c453c8c99cb6ee92d6956a1f00c701aa832095b27048009b2ece9095b","first_computed_at":"2026-07-05T08:54:00.248216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:54:00.248216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TUrxQpDcl1ehLUJgSbkglVtk7tUE+Xh56126V6+fU5R2tCnIOx8ol80oDgA6f/MiSgPD7Czr9FYU9CvBVkeQCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:54:00.248722Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.13182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16f9c5e1da3e0169be7180ef2d97f8a0bf195d006c3f3d73203ad126839d3d14","sha256:78a3d1711f116bb2e440315e6362cd4a8be2f169f932944a422e1a789cae5f44"],"state_sha256":"0af5344f74ad96ecd0575cb9df3c61c65efc7d4953a26250598929e7eb6109dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5aEwvnXLk+tyMmqCI3B3YOu4qVIVbfFnvdz8PKnBjpZIfDO3x4579ibeXT3ORSFhBbYKyeQL5HlawL5o7n9MDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T06:18:54.401424Z","bundle_sha256":"ff933a9d3ffd25f2f0e03d3bf8383068e2cb3a4f83148f8da128a4c41c351bc7"}}