{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:FINFVDUVGVL3EUHTT4BHUINYTI","short_pith_number":"pith:FINFVDUV","canonical_record":{"source":{"id":"2011.14142","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2020-11-28T14:55:13Z","cross_cats_sorted":[],"title_canon_sha256":"96c145b3dde355ef7ed9c940a2e8f0019968d4b43de799a5a43db33240c38359","abstract_canon_sha256":"f6effd3e0096930841dc7fbd1fde249dec4484fcffd63bcdd9fdc99bb02a4a34"},"schema_version":"1.0"},"canonical_sha256":"2a1a5a8e953557b250f39f027a21b89a24e954515f89729091338763e3f6b1ae","source":{"kind":"arxiv","id":"2011.14142","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.14142","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"2011.14142v1","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.14142","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"FINFVDUVGVL3","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_16","alias_value":"FINFVDUVGVL3EUHT","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_8","alias_value":"FINFVDUV","created_at":"2026-07-05T01:55:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:FINFVDUVGVL3EUHTT4BHUINYTI","target":"record","payload":{"canonical_record":{"source":{"id":"2011.14142","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2020-11-28T14:55:13Z","cross_cats_sorted":[],"title_canon_sha256":"96c145b3dde355ef7ed9c940a2e8f0019968d4b43de799a5a43db33240c38359","abstract_canon_sha256":"f6effd3e0096930841dc7fbd1fde249dec4484fcffd63bcdd9fdc99bb02a4a34"},"schema_version":"1.0"},"canonical_sha256":"2a1a5a8e953557b250f39f027a21b89a24e954515f89729091338763e3f6b1ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:55:17.694639Z","signature_b64":"FXs39lUkt6mrb5s+NP4KV48Vyy6r2GUUPXOXbWN4W2fyWU7vMJtk0IbZ/F/B0HNlnnYeIqrGVDRbFsbGDDBOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a1a5a8e953557b250f39f027a21b89a24e954515f89729091338763e3f6b1ae","last_reissued_at":"2026-07-05T01:55:17.694289Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:55:17.694289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.14142","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":"2026-07-05T01:55:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjyODOr5sCgRSy0GLGynaIqyjSZYBYcrpd0BrXVhTe7RYGRa853H0hfa01okpe1dmE4+LZ6A/QrcLH4jnEjBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T22:52:04.356488Z"},"content_sha256":"6947b7643804e811c8e35189784a31230e0263085fc638c02da5868e9d7b34ea","schema_version":"1.0","event_id":"sha256:6947b7643804e811c8e35189784a31230e0263085fc638c02da5868e9d7b34ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:FINFVDUVGVL3EUHTT4BHUINYTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimizing cycles in tournaments and normalized $q$-norms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma, Tianyun Tang","submitted_at":"2020-11-28T14:55:13Z","abstract_excerpt":"Akin to the Erd\\H{o}s-Rademacher problem, Linial and Morgenstern made the following conjecture in tournaments: for any $d\\in (0,1]$, among all $n$-vertex tournaments with $d\\binom{n}{3}$ many 3-cycles, the number of 4-cycles is asymptotically minimized by a special random blow-up of a transitive tournament. Recently, Chan, Grzesik, Kr\\'al' and Noel introduced spectrum analysis of adjacency matrices of tournaments in this study, and confirmed this for $d\\geq 1/36$.\n  In this paper, we investigate the analogous problem of minimizing the number of cycles of a given length. We prove that for integ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.14142","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/2011.14142/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":"2026-07-05T01:55:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDNMi3SjxRxuSF7DS8gIp1zCWzA3i16O+chqUPKbbJSQOq4aJxdiIxqeavJPHtyR1yxv6C2Qdl8CbM88NSn5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T22:52:04.356868Z"},"content_sha256":"aaa3a51a83ea5911159cfe7296e53a2ba4f1d559741b8c51712955bb60439ed6","schema_version":"1.0","event_id":"sha256:aaa3a51a83ea5911159cfe7296e53a2ba4f1d559741b8c51712955bb60439ed6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FINFVDUVGVL3EUHTT4BHUINYTI/bundle.json","state_url":"https://pith.science/pith/FINFVDUVGVL3EUHTT4BHUINYTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FINFVDUVGVL3EUHTT4BHUINYTI/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":"2026-07-13T22:52:04Z","links":{"resolver":"https://pith.science/pith/FINFVDUVGVL3EUHTT4BHUINYTI","bundle":"https://pith.science/pith/FINFVDUVGVL3EUHTT4BHUINYTI/bundle.json","state":"https://pith.science/pith/FINFVDUVGVL3EUHTT4BHUINYTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FINFVDUVGVL3EUHTT4BHUINYTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FINFVDUVGVL3EUHTT4BHUINYTI","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":"f6effd3e0096930841dc7fbd1fde249dec4484fcffd63bcdd9fdc99bb02a4a34","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2020-11-28T14:55:13Z","title_canon_sha256":"96c145b3dde355ef7ed9c940a2e8f0019968d4b43de799a5a43db33240c38359"},"schema_version":"1.0","source":{"id":"2011.14142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.14142","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"2011.14142v1","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.14142","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"FINFVDUVGVL3","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_16","alias_value":"FINFVDUVGVL3EUHT","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_8","alias_value":"FINFVDUV","created_at":"2026-07-05T01:55:17Z"}],"graph_snapshots":[{"event_id":"sha256:aaa3a51a83ea5911159cfe7296e53a2ba4f1d559741b8c51712955bb60439ed6","target":"graph","created_at":"2026-07-05T01:55:17Z","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/2011.14142/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Akin to the Erd\\H{o}s-Rademacher problem, Linial and Morgenstern made the following conjecture in tournaments: for any $d\\in (0,1]$, among all $n$-vertex tournaments with $d\\binom{n}{3}$ many 3-cycles, the number of 4-cycles is asymptotically minimized by a special random blow-up of a transitive tournament. Recently, Chan, Grzesik, Kr\\'al' and Noel introduced spectrum analysis of adjacency matrices of tournaments in this study, and confirmed this for $d\\geq 1/36$.\n  In this paper, we investigate the analogous problem of minimizing the number of cycles of a given length. We prove that for integ","authors_text":"Jie Ma, Tianyun Tang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2020-11-28T14:55:13Z","title":"Minimizing cycles in tournaments and normalized $q$-norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.14142","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":"sha256:6947b7643804e811c8e35189784a31230e0263085fc638c02da5868e9d7b34ea","target":"record","created_at":"2026-07-05T01:55:17Z","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":"f6effd3e0096930841dc7fbd1fde249dec4484fcffd63bcdd9fdc99bb02a4a34","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2020-11-28T14:55:13Z","title_canon_sha256":"96c145b3dde355ef7ed9c940a2e8f0019968d4b43de799a5a43db33240c38359"},"schema_version":"1.0","source":{"id":"2011.14142","kind":"arxiv","version":1}},"canonical_sha256":"2a1a5a8e953557b250f39f027a21b89a24e954515f89729091338763e3f6b1ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a1a5a8e953557b250f39f027a21b89a24e954515f89729091338763e3f6b1ae","first_computed_at":"2026-07-05T01:55:17.694289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:55:17.694289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXs39lUkt6mrb5s+NP4KV48Vyy6r2GUUPXOXbWN4W2fyWU7vMJtk0IbZ/F/B0HNlnnYeIqrGVDRbFsbGDDBOBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:55:17.694639Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.14142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6947b7643804e811c8e35189784a31230e0263085fc638c02da5868e9d7b34ea","sha256:aaa3a51a83ea5911159cfe7296e53a2ba4f1d559741b8c51712955bb60439ed6"],"state_sha256":"e6544fdbeee49782461fb44525c9e62e3609ad13deae101c68743e1a4b008a7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6Gd9JjeYgX0ILeMj/8sY2XzfOhq2SSZP3tErF8t9/0qWSXRQINzKkvhbj+A7PlgQ3iCJK0CDd6vG59dP1esDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T22:52:04.358962Z","bundle_sha256":"17bf972cc024c923debc26ccc2e4b0642d293e4f0250b1586abd65b5df075825"}}