{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I2NZ5XWWCDXIEPJ4SRYQ3FGJX2","short_pith_number":"pith:I2NZ5XWW","canonical_record":{"source":{"id":"1605.09343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-30T17:54:54Z","cross_cats_sorted":[],"title_canon_sha256":"7d2ae1af9518ba888d2e8526b81fcdaa01ddd3b877125296fbd2d7ddbbd37743","abstract_canon_sha256":"b4896744de9bbc94eae53fd60a052cb60794ce40fe9a187afaaf83866d061340"},"schema_version":"1.0"},"canonical_sha256":"469b9eded610ee823d3c94710d94c9be9bb828430d97a7f865a0ef3f7d7ea53a","source":{"kind":"arxiv","id":"1605.09343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09343","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09343v1","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09343","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"I2NZ5XWWCDXI","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I2NZ5XWWCDXIEPJ4","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I2NZ5XWW","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I2NZ5XWWCDXIEPJ4SRYQ3FGJX2","target":"record","payload":{"canonical_record":{"source":{"id":"1605.09343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-30T17:54:54Z","cross_cats_sorted":[],"title_canon_sha256":"7d2ae1af9518ba888d2e8526b81fcdaa01ddd3b877125296fbd2d7ddbbd37743","abstract_canon_sha256":"b4896744de9bbc94eae53fd60a052cb60794ce40fe9a187afaaf83866d061340"},"schema_version":"1.0"},"canonical_sha256":"469b9eded610ee823d3c94710d94c9be9bb828430d97a7f865a0ef3f7d7ea53a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:21.352566Z","signature_b64":"pdoh7zZIwC89mMcvISHn5FHoizkjLi/1q7byfn7n3fPVkuSa7AAueirlGGCkXMN4rwcGga1qtNqoX6HISlfpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"469b9eded610ee823d3c94710d94c9be9bb828430d97a7f865a0ef3f7d7ea53a","last_reissued_at":"2026-05-18T01:13:21.352050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:21.352050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.09343","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":"2026-05-18T01:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pZxtsHQTakFGWbSrmI0nK2gAk/V/uitKZuG1BM2vo2Ghm2SmJTEIX2aQWw7DBRfNWo2z4WqaFpg+QDg9bhewDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:02:37.734292Z"},"content_sha256":"34e03c70231327e7c696a46f58da73631c71fd8386150207fb0e06e73d8222f2","schema_version":"1.0","event_id":"sha256:34e03c70231327e7c696a46f58da73631c71fd8386150207fb0e06e73d8222f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I2NZ5XWWCDXIEPJ4SRYQ3FGJX2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coloring Factors of Substitutive Infinite Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Bernardino, M. Silva, R. Pacheco","submitted_at":"2016-05-30T17:54:54Z","abstract_excerpt":"In this paper, we consider infinite words that arise as fixed points of primitive substitutions on a finite alphabet and finite colorings of their factors. Any such infinite word exhibits a \"hierarchal structure\" that will allow us to define, under the additional condition of strong recognizability, certain remarkable finite colorings of its factors. In particular, we generalize two combinatorial results by Justin and Pirillo concerning arbitrarily large monochromatic $k$-powers occurring in infinite words, in view of a recent paper by de Luca, Pribavkina and Zamboni, we will give new examples"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09343","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":"2026-05-18T01:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0T/W+q4Nja+6dkv+/4g+x8rumw2b9CkxF740taVbPdvsqx2li5XONpSP5HZ5RdYXARwepUqP8eizYJs4Qsu7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:02:37.734660Z"},"content_sha256":"2531c050ff279e5170c25e076a087a3656879bed797b773f79faf5799ff0d310","schema_version":"1.0","event_id":"sha256:2531c050ff279e5170c25e076a087a3656879bed797b773f79faf5799ff0d310"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2NZ5XWWCDXIEPJ4SRYQ3FGJX2/bundle.json","state_url":"https://pith.science/pith/I2NZ5XWWCDXIEPJ4SRYQ3FGJX2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2NZ5XWWCDXIEPJ4SRYQ3FGJX2/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":"2026-06-05T11:02:37Z","links":{"resolver":"https://pith.science/pith/I2NZ5XWWCDXIEPJ4SRYQ3FGJX2","bundle":"https://pith.science/pith/I2NZ5XWWCDXIEPJ4SRYQ3FGJX2/bundle.json","state":"https://pith.science/pith/I2NZ5XWWCDXIEPJ4SRYQ3FGJX2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2NZ5XWWCDXIEPJ4SRYQ3FGJX2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I2NZ5XWWCDXIEPJ4SRYQ3FGJX2","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":"b4896744de9bbc94eae53fd60a052cb60794ce40fe9a187afaaf83866d061340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-30T17:54:54Z","title_canon_sha256":"7d2ae1af9518ba888d2e8526b81fcdaa01ddd3b877125296fbd2d7ddbbd37743"},"schema_version":"1.0","source":{"id":"1605.09343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09343","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09343v1","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09343","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"I2NZ5XWWCDXI","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I2NZ5XWWCDXIEPJ4","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I2NZ5XWW","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:2531c050ff279e5170c25e076a087a3656879bed797b773f79faf5799ff0d310","target":"graph","created_at":"2026-05-18T01:13:21Z","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":"In this paper, we consider infinite words that arise as fixed points of primitive substitutions on a finite alphabet and finite colorings of their factors. Any such infinite word exhibits a \"hierarchal structure\" that will allow us to define, under the additional condition of strong recognizability, certain remarkable finite colorings of its factors. In particular, we generalize two combinatorial results by Justin and Pirillo concerning arbitrarily large monochromatic $k$-powers occurring in infinite words, in view of a recent paper by de Luca, Pribavkina and Zamboni, we will give new examples","authors_text":"A. Bernardino, M. Silva, R. Pacheco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-30T17:54:54Z","title":"Coloring Factors of Substitutive Infinite Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09343","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":"sha256:34e03c70231327e7c696a46f58da73631c71fd8386150207fb0e06e73d8222f2","target":"record","created_at":"2026-05-18T01:13:21Z","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":"b4896744de9bbc94eae53fd60a052cb60794ce40fe9a187afaaf83866d061340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-30T17:54:54Z","title_canon_sha256":"7d2ae1af9518ba888d2e8526b81fcdaa01ddd3b877125296fbd2d7ddbbd37743"},"schema_version":"1.0","source":{"id":"1605.09343","kind":"arxiv","version":1}},"canonical_sha256":"469b9eded610ee823d3c94710d94c9be9bb828430d97a7f865a0ef3f7d7ea53a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"469b9eded610ee823d3c94710d94c9be9bb828430d97a7f865a0ef3f7d7ea53a","first_computed_at":"2026-05-18T01:13:21.352050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:21.352050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pdoh7zZIwC89mMcvISHn5FHoizkjLi/1q7byfn7n3fPVkuSa7AAueirlGGCkXMN4rwcGga1qtNqoX6HISlfpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:21.352566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34e03c70231327e7c696a46f58da73631c71fd8386150207fb0e06e73d8222f2","sha256:2531c050ff279e5170c25e076a087a3656879bed797b773f79faf5799ff0d310"],"state_sha256":"612db02d281f8f640d7cb485b3102b46eab93ebcab16c305afee5d824bea5b51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tLYIlAVZstyzpBIIFMhmex4lzhzHAVF8slThNz4KxfxNysM7oFBF9aqnT13MaQBkKQHQIESJL6xX8L3TwVfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:02:37.736726Z","bundle_sha256":"8c91ba2db2f63e5680533c39fd220347c2e4a8108c1a4241d2cc6ec99cb92125"}}