{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IS22YZDIB5UTDRE5RAV53JXZCS","short_pith_number":"pith:IS22YZDI","canonical_record":{"source":{"id":"1908.03315","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T04:58:27Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"bbfbd9dc72a622cbda13c994f290c28993d58bf59f1e7e4dcaf13f633142036f","abstract_canon_sha256":"1281740e4f49d15841786782a606a086fbf02e78181e5cf4116e177c0300a9e1"},"schema_version":"1.0"},"canonical_sha256":"44b5ac64680f6931c49d882bdda6f9149a3ab6a4d78461051a4912da44e7cd22","source":{"kind":"arxiv","id":"1908.03315","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03315","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03315v3","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03315","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"IS22YZDIB5UT","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"IS22YZDIB5UTDRE5","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"IS22YZDI","created_at":"2026-07-05T02:21:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IS22YZDIB5UTDRE5RAV53JXZCS","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03315","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T04:58:27Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"bbfbd9dc72a622cbda13c994f290c28993d58bf59f1e7e4dcaf13f633142036f","abstract_canon_sha256":"1281740e4f49d15841786782a606a086fbf02e78181e5cf4116e177c0300a9e1"},"schema_version":"1.0"},"canonical_sha256":"44b5ac64680f6931c49d882bdda6f9149a3ab6a4d78461051a4912da44e7cd22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:21:49.728622Z","signature_b64":"wh9AckM2+tvOwLiwPbd8D7mUMhIZECJpBMhCsbfwagIn1BzJBpyYtxHTHgnmx6pj8xtbupKCcRZcVp9srfW4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44b5ac64680f6931c49d882bdda6f9149a3ab6a4d78461051a4912da44e7cd22","last_reissued_at":"2026-07-05T02:21:49.728122Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:21:49.728122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03315","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kp2Bb50rFof8+8z0G+QTM7EsZRzcFyVPJlSQtrSF63Mdc2tuBdzStdRnwJ/P08fyrAtZuuKyBNq5lQqjYrVYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:11:21.906255Z"},"content_sha256":"e0a3ad5fabea5cb6bb0cc85a98f0bb7cd031021cdcaf9497571c61dbc6e4e578","schema_version":"1.0","event_id":"sha256:e0a3ad5fabea5cb6bb0cc85a98f0bb7cd031021cdcaf9497571c61dbc6e4e578"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IS22YZDIB5UTDRE5RAV53JXZCS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant systems of representatives, or The cost of symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Anton A. Klyachko, Natalia M. Luneva","submitted_at":"2019-08-09T04:58:27Z","abstract_excerpt":"Suppose that one can destroy all 100-gons in a graph by removing 2019 edges. How many edges must be removed to destroy all 100-gons in such a way that the set of removed edges is invariant with respect to all automorphisms the initial graph? This paper contains solutions to such kind of problems. Several open questions are raised."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03315","kind":"arxiv","version":3},"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/1908.03315/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":"2026-07-05T02:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3HRcNNqiIN5DV4bO3dhdPv6CJMVZsyMgoh65lTOerdomFKxUlWpNMDQPz1KCQlnA5y9m9DdQnozdpCaCcPiCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:11:21.907029Z"},"content_sha256":"b3d51ce5ef3368e40a0521f3a70b29e834ee8882629929c1673ecab8e6a21fd4","schema_version":"1.0","event_id":"sha256:b3d51ce5ef3368e40a0521f3a70b29e834ee8882629929c1673ecab8e6a21fd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IS22YZDIB5UTDRE5RAV53JXZCS/bundle.json","state_url":"https://pith.science/pith/IS22YZDIB5UTDRE5RAV53JXZCS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IS22YZDIB5UTDRE5RAV53JXZCS/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":"2026-08-16T14:11:21Z","links":{"resolver":"https://pith.science/pith/IS22YZDIB5UTDRE5RAV53JXZCS","bundle":"https://pith.science/pith/IS22YZDIB5UTDRE5RAV53JXZCS/bundle.json","state":"https://pith.science/pith/IS22YZDIB5UTDRE5RAV53JXZCS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IS22YZDIB5UTDRE5RAV53JXZCS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IS22YZDIB5UTDRE5RAV53JXZCS","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":"1281740e4f49d15841786782a606a086fbf02e78181e5cf4116e177c0300a9e1","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T04:58:27Z","title_canon_sha256":"bbfbd9dc72a622cbda13c994f290c28993d58bf59f1e7e4dcaf13f633142036f"},"schema_version":"1.0","source":{"id":"1908.03315","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03315","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03315v3","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03315","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"IS22YZDIB5UT","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"IS22YZDIB5UTDRE5","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"IS22YZDI","created_at":"2026-07-05T02:21:49Z"}],"graph_snapshots":[{"event_id":"sha256:b3d51ce5ef3368e40a0521f3a70b29e834ee8882629929c1673ecab8e6a21fd4","target":"graph","created_at":"2026-07-05T02:21:49Z","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/1908.03315/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose that one can destroy all 100-gons in a graph by removing 2019 edges. How many edges must be removed to destroy all 100-gons in such a way that the set of removed edges is invariant with respect to all automorphisms the initial graph? This paper contains solutions to such kind of problems. Several open questions are raised.","authors_text":"Anton A. Klyachko, Natalia M. Luneva","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T04:58:27Z","title":"Invariant systems of representatives, or The cost of symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03315","kind":"arxiv","version":3},"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:e0a3ad5fabea5cb6bb0cc85a98f0bb7cd031021cdcaf9497571c61dbc6e4e578","target":"record","created_at":"2026-07-05T02:21:49Z","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":"1281740e4f49d15841786782a606a086fbf02e78181e5cf4116e177c0300a9e1","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T04:58:27Z","title_canon_sha256":"bbfbd9dc72a622cbda13c994f290c28993d58bf59f1e7e4dcaf13f633142036f"},"schema_version":"1.0","source":{"id":"1908.03315","kind":"arxiv","version":3}},"canonical_sha256":"44b5ac64680f6931c49d882bdda6f9149a3ab6a4d78461051a4912da44e7cd22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44b5ac64680f6931c49d882bdda6f9149a3ab6a4d78461051a4912da44e7cd22","first_computed_at":"2026-07-05T02:21:49.728122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:21:49.728122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wh9AckM2+tvOwLiwPbd8D7mUMhIZECJpBMhCsbfwagIn1BzJBpyYtxHTHgnmx6pj8xtbupKCcRZcVp9srfW4CA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:21:49.728622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03315","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0a3ad5fabea5cb6bb0cc85a98f0bb7cd031021cdcaf9497571c61dbc6e4e578","sha256:b3d51ce5ef3368e40a0521f3a70b29e834ee8882629929c1673ecab8e6a21fd4"],"state_sha256":"ce48ed2ff5bad5f61cab37733585633f604409af90f7e53c88798fc4dd04fc84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bPCITVsKuqhWt4+Ww6OumK3DHMsVrblbYjnbQRfRovTyBMtTibBjAaB9wCDDTwuRXPrZKoxVyf7E6vIp8mHPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:11:21.913597Z","bundle_sha256":"f80aee8ab9b38765bb47512b96d483538a9c818b855cfe50dd16152a6790cfb1"}}