{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:D7EC5ILFPPXZQXO5OA62ROZYPU","short_pith_number":"pith:D7EC5ILF","canonical_record":{"source":{"id":"2605.20265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-05-18T19:06:36Z","cross_cats_sorted":[],"title_canon_sha256":"07c58ada142754eb8792ed810b5179ad3fdca0a7f34129fbf1a894d499e3fae9","abstract_canon_sha256":"166bdb0466ee247a283b3a8efd849fda1e692d81a8d0e5d84c0f7a68e12d82cf"},"schema_version":"1.0"},"canonical_sha256":"1fc82ea1657bef985ddd703da8bb387d170fdd08646aec51ccbc40cc93dc8863","source":{"kind":"arxiv","id":"2605.20265","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20265","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20265v1","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20265","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"pith_short_12","alias_value":"D7EC5ILFPPXZ","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"pith_short_16","alias_value":"D7EC5ILFPPXZQXO5","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"pith_short_8","alias_value":"D7EC5ILF","created_at":"2026-05-21T00:04:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:D7EC5ILFPPXZQXO5OA62ROZYPU","target":"record","payload":{"canonical_record":{"source":{"id":"2605.20265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-05-18T19:06:36Z","cross_cats_sorted":[],"title_canon_sha256":"07c58ada142754eb8792ed810b5179ad3fdca0a7f34129fbf1a894d499e3fae9","abstract_canon_sha256":"166bdb0466ee247a283b3a8efd849fda1e692d81a8d0e5d84c0f7a68e12d82cf"},"schema_version":"1.0"},"canonical_sha256":"1fc82ea1657bef985ddd703da8bb387d170fdd08646aec51ccbc40cc93dc8863","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T00:04:23.182340Z","signature_b64":"0rty5S3i5yuVFNAbFKyoIFTOLVMH4eFKd94w3gc6zKkV3i2v51upOQOLbVdKE4XzQhdfWvrKqkbo3H1SMa+rDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fc82ea1657bef985ddd703da8bb387d170fdd08646aec51ccbc40cc93dc8863","last_reissued_at":"2026-05-21T00:04:23.181870Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T00:04:23.181870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.20265","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":"2026-05-21T00:04:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J2lK4T/w5ZyCJNN/VcnQZpOOYHpCt/6iMqx5yVz/00XfPxv8znVHrQ3tMpKRfbCLaE39UFwCk7qeJzthKHSNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:26:07.601862Z"},"content_sha256":"79a78f785c3737caba3540b07e67b7f4fb4697b0d42c919a8e629931e4b14126","schema_version":"1.0","event_id":"sha256:79a78f785c3737caba3540b07e67b7f4fb4697b0d42c919a8e629931e4b14126"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:D7EC5ILFPPXZQXO5OA62ROZYPU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bitwise Triangular Coordinates for Central Products of Quaternion Groups: Floretion Base Vectors, Digitwise S3-Actions, and Centralizer Tiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Creighton Dement","submitted_at":"2026-05-18T19:06:36Z","abstract_excerpt":"This note studies a concrete bitwise and triangular coordinate model for the central product of n copies of the quaternion group Q8. The positive basis elements are words of length n in the alphabet {1, 2, 4, 7}, identified with i, j, k, and the identity element e. The signed basis group Fn is the corresponding central product of n copies of Q8, and the real algebra generated by the basis words is H^{\\otimes n}. The contribution is the coordinate model: in this basis, Boolean multiplication, recursive triangular tilings, digitwise S3-actions, reflection anti-automorphisms, parity cancellation,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20265","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/2605.20265/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":"2026-05-21T00:04:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7JASe2fz12NRdS42EVSWPhhasrp4Zg5ZhTrTry73Fbw27LD0ybxIe44vEUPW/+BCuPtDRppRxJcqD3ZwxGwzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:26:07.602241Z"},"content_sha256":"5d24ba3be440329ffed4d0e0f959092a559069df032b3aa8102f385302088b9e","schema_version":"1.0","event_id":"sha256:5d24ba3be440329ffed4d0e0f959092a559069df032b3aa8102f385302088b9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D7EC5ILFPPXZQXO5OA62ROZYPU/bundle.json","state_url":"https://pith.science/pith/D7EC5ILFPPXZQXO5OA62ROZYPU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D7EC5ILFPPXZQXO5OA62ROZYPU/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":"2026-06-04T10:26:07Z","links":{"resolver":"https://pith.science/pith/D7EC5ILFPPXZQXO5OA62ROZYPU","bundle":"https://pith.science/pith/D7EC5ILFPPXZQXO5OA62ROZYPU/bundle.json","state":"https://pith.science/pith/D7EC5ILFPPXZQXO5OA62ROZYPU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D7EC5ILFPPXZQXO5OA62ROZYPU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D7EC5ILFPPXZQXO5OA62ROZYPU","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":"166bdb0466ee247a283b3a8efd849fda1e692d81a8d0e5d84c0f7a68e12d82cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-05-18T19:06:36Z","title_canon_sha256":"07c58ada142754eb8792ed810b5179ad3fdca0a7f34129fbf1a894d499e3fae9"},"schema_version":"1.0","source":{"id":"2605.20265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20265","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20265v1","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20265","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"pith_short_12","alias_value":"D7EC5ILFPPXZ","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"pith_short_16","alias_value":"D7EC5ILFPPXZQXO5","created_at":"2026-05-21T00:04:23Z"},{"alias_kind":"pith_short_8","alias_value":"D7EC5ILF","created_at":"2026-05-21T00:04:23Z"}],"graph_snapshots":[{"event_id":"sha256:5d24ba3be440329ffed4d0e0f959092a559069df032b3aa8102f385302088b9e","target":"graph","created_at":"2026-05-21T00:04:23Z","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/2605.20265/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note studies a concrete bitwise and triangular coordinate model for the central product of n copies of the quaternion group Q8. The positive basis elements are words of length n in the alphabet {1, 2, 4, 7}, identified with i, j, k, and the identity element e. The signed basis group Fn is the corresponding central product of n copies of Q8, and the real algebra generated by the basis words is H^{\\otimes n}. The contribution is the coordinate model: in this basis, Boolean multiplication, recursive triangular tilings, digitwise S3-actions, reflection anti-automorphisms, parity cancellation,","authors_text":"Creighton Dement","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-05-18T19:06:36Z","title":"Bitwise Triangular Coordinates for Central Products of Quaternion Groups: Floretion Base Vectors, Digitwise S3-Actions, and Centralizer Tiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20265","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":"sha256:79a78f785c3737caba3540b07e67b7f4fb4697b0d42c919a8e629931e4b14126","target":"record","created_at":"2026-05-21T00:04:23Z","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":"166bdb0466ee247a283b3a8efd849fda1e692d81a8d0e5d84c0f7a68e12d82cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-05-18T19:06:36Z","title_canon_sha256":"07c58ada142754eb8792ed810b5179ad3fdca0a7f34129fbf1a894d499e3fae9"},"schema_version":"1.0","source":{"id":"2605.20265","kind":"arxiv","version":1}},"canonical_sha256":"1fc82ea1657bef985ddd703da8bb387d170fdd08646aec51ccbc40cc93dc8863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fc82ea1657bef985ddd703da8bb387d170fdd08646aec51ccbc40cc93dc8863","first_computed_at":"2026-05-21T00:04:23.181870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T00:04:23.181870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0rty5S3i5yuVFNAbFKyoIFTOLVMH4eFKd94w3gc6zKkV3i2v51upOQOLbVdKE4XzQhdfWvrKqkbo3H1SMa+rDQ==","signature_status":"signed_v1","signed_at":"2026-05-21T00:04:23.182340Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79a78f785c3737caba3540b07e67b7f4fb4697b0d42c919a8e629931e4b14126","sha256:5d24ba3be440329ffed4d0e0f959092a559069df032b3aa8102f385302088b9e"],"state_sha256":"a0d2a54a9c19dcfd043c20c30641028a180f012a2bfd5267e64626bfbe8bb89f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGZ9Jw5ZMACC3yC2oYrB7Nw8hOkIjgvB9XCoQZbBXDrP8IUFJUvaPIeyPktRiahibHxUZ2z+KL5US4LXf9FnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:26:07.604468Z","bundle_sha256":"adf152415181bbbe35b1e6aa2f6f7f8c19c3f2c7afa81895b28a064e87db6922"}}