{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4IYW4WZPDD4D6GKSXRVF535773","short_pith_number":"pith:4IYW4WZP","canonical_record":{"source":{"id":"1805.10042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-25T08:54:26Z","cross_cats_sorted":["cs.DM","cs.FL"],"title_canon_sha256":"7f81b5a04d9bca6771a5201dcbe904964e46483316fbe9695a387be6c23bb9d0","abstract_canon_sha256":"3766e5a6dfc7ca25af1575da593682c38c97cc87681210b6e7c7a9781e475983"},"schema_version":"1.0"},"canonical_sha256":"e2316e5b2f18f83f1952bc6a5eefbffeef4930ddd60756b5da93c161c6bfb7ed","source":{"kind":"arxiv","id":"1805.10042","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10042","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10042v1","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10042","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"4IYW4WZPDD4D","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4IYW4WZPDD4D6GKS","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4IYW4WZP","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4IYW4WZPDD4D6GKSXRVF535773","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-25T08:54:26Z","cross_cats_sorted":["cs.DM","cs.FL"],"title_canon_sha256":"7f81b5a04d9bca6771a5201dcbe904964e46483316fbe9695a387be6c23bb9d0","abstract_canon_sha256":"3766e5a6dfc7ca25af1575da593682c38c97cc87681210b6e7c7a9781e475983"},"schema_version":"1.0"},"canonical_sha256":"e2316e5b2f18f83f1952bc6a5eefbffeef4930ddd60756b5da93c161c6bfb7ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:58.422333Z","signature_b64":"brFp7NPrYMTYjLGI+EhLMIzU/ZM3Iu42cCRwWIWqquhx6cWX02Ikt9YUIvT62ZhVW2fVjKPStrfWabU/+sl9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2316e5b2f18f83f1952bc6a5eefbffeef4930ddd60756b5da93c161c6bfb7ed","last_reissued_at":"2026-05-18T00:14:58.421810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:58.421810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10042","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":"2026-05-18T00:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"blqctVd5klG4MLoWtHVG513KsgdtbHilxvGxPUJLMoKyhdi79KucZqAvww/+Nxx8jOeFAUB/YwjNQNRvy1WEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:57:02.812842Z"},"content_sha256":"eebdb2402bac9ecadfa8a755edd040cb36d30e5e7f698358e39151e74ae614a2","schema_version":"1.0","event_id":"sha256:eebdb2402bac9ecadfa8a755edd040cb36d30e5e7f698358e39151e74ae614a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4IYW4WZPDD4D6GKSXRVF535773","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms for Anti-Powers in Strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL"],"primary_cat":"cs.DS","authors_text":"Gabriele Fici, Golnaz Badkobeh, Simon J. Puglisi","submitted_at":"2018-05-25T08:54:26Z","abstract_excerpt":"A string $S[1,n]$ is a power (or tandem repeat) of order $k$ and period $n/k$ if it can decomposed into $k$ consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient computation have wide application and are heavily studied. Recently, Fici et al. (Proc. ICALP 2016) defined an {\\em anti-power} of order $k$ to be a string composed of $k$ pairwise-distinct blocks of the same length ($n/k$, called {\\em anti-period}). Anti-powers are a natural converse to powers, and are objects of combinatorial interest in their own righ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10042","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":"2026-05-18T00:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FSh6wEydobTQmcXUOIKUpLkKLN7iFLJplkTMMmbPBN2xXMkviYUpzmyGLkmbiUWKVm4Qd0GZEt2Bs4rqULPVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:57:02.813531Z"},"content_sha256":"3ec0676cf172087bda776945ece238cc535a2fec46dfcc737bebce46a30d48d3","schema_version":"1.0","event_id":"sha256:3ec0676cf172087bda776945ece238cc535a2fec46dfcc737bebce46a30d48d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4IYW4WZPDD4D6GKSXRVF535773/bundle.json","state_url":"https://pith.science/pith/4IYW4WZPDD4D6GKSXRVF535773/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4IYW4WZPDD4D6GKSXRVF535773/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":"2026-05-26T16:57:02Z","links":{"resolver":"https://pith.science/pith/4IYW4WZPDD4D6GKSXRVF535773","bundle":"https://pith.science/pith/4IYW4WZPDD4D6GKSXRVF535773/bundle.json","state":"https://pith.science/pith/4IYW4WZPDD4D6GKSXRVF535773/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4IYW4WZPDD4D6GKSXRVF535773/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4IYW4WZPDD4D6GKSXRVF535773","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":"3766e5a6dfc7ca25af1575da593682c38c97cc87681210b6e7c7a9781e475983","cross_cats_sorted":["cs.DM","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-25T08:54:26Z","title_canon_sha256":"7f81b5a04d9bca6771a5201dcbe904964e46483316fbe9695a387be6c23bb9d0"},"schema_version":"1.0","source":{"id":"1805.10042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10042","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10042v1","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10042","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"4IYW4WZPDD4D","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4IYW4WZPDD4D6GKS","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4IYW4WZP","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:3ec0676cf172087bda776945ece238cc535a2fec46dfcc737bebce46a30d48d3","target":"graph","created_at":"2026-05-18T00:14:58Z","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":"A string $S[1,n]$ is a power (or tandem repeat) of order $k$ and period $n/k$ if it can decomposed into $k$ consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient computation have wide application and are heavily studied. Recently, Fici et al. (Proc. ICALP 2016) defined an {\\em anti-power} of order $k$ to be a string composed of $k$ pairwise-distinct blocks of the same length ($n/k$, called {\\em anti-period}). Anti-powers are a natural converse to powers, and are objects of combinatorial interest in their own righ","authors_text":"Gabriele Fici, Golnaz Badkobeh, Simon J. Puglisi","cross_cats":["cs.DM","cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-25T08:54:26Z","title":"Algorithms for Anti-Powers in Strings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10042","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:eebdb2402bac9ecadfa8a755edd040cb36d30e5e7f698358e39151e74ae614a2","target":"record","created_at":"2026-05-18T00:14:58Z","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":"3766e5a6dfc7ca25af1575da593682c38c97cc87681210b6e7c7a9781e475983","cross_cats_sorted":["cs.DM","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-25T08:54:26Z","title_canon_sha256":"7f81b5a04d9bca6771a5201dcbe904964e46483316fbe9695a387be6c23bb9d0"},"schema_version":"1.0","source":{"id":"1805.10042","kind":"arxiv","version":1}},"canonical_sha256":"e2316e5b2f18f83f1952bc6a5eefbffeef4930ddd60756b5da93c161c6bfb7ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2316e5b2f18f83f1952bc6a5eefbffeef4930ddd60756b5da93c161c6bfb7ed","first_computed_at":"2026-05-18T00:14:58.421810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:58.421810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"brFp7NPrYMTYjLGI+EhLMIzU/ZM3Iu42cCRwWIWqquhx6cWX02Ikt9YUIvT62ZhVW2fVjKPStrfWabU/+sl9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:58.422333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eebdb2402bac9ecadfa8a755edd040cb36d30e5e7f698358e39151e74ae614a2","sha256:3ec0676cf172087bda776945ece238cc535a2fec46dfcc737bebce46a30d48d3"],"state_sha256":"17fc388c21cb6e4b5d24869abeb1af1a236d3c428ead1a0dacaac9d86e2e01ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZiVFU7YKDICbCaCTqiA+tcZPObX7U6RTrCn2Qh9aweCabtUBa5ehgFhyPxVtj5B2q1CQtdnzq+ldBopmCCiRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:57:02.817069Z","bundle_sha256":"65c81f630462b570622c46f1861453b18a6ad0a24e0f1ea506758dde745df758"}}