{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:BEPK4U3IKRZFYSNNMJDVTM3NNH","short_pith_number":"pith:BEPK4U3I","canonical_record":{"source":{"id":"2201.06923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2021-12-14T17:18:53Z","cross_cats_sorted":["cs.LG","gr-qc"],"title_canon_sha256":"46fd875250a358bf765b451e74b7dfe122513841184fd530bb1f9c0db6073ea1","abstract_canon_sha256":"14267747ad7ea2e57b5212889fda997e69819afc05021c257bbb358382d4ceb4"},"schema_version":"1.0"},"canonical_sha256":"091eae536854725c49ad624759b36d69fa638c0a61457bbe2f9ca3dbef9152a4","source":{"kind":"arxiv","id":"2201.06923","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.06923","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"2201.06923v1","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.06923","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"BEPK4U3IKRZF","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"pith_short_16","alias_value":"BEPK4U3IKRZFYSNN","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"pith_short_8","alias_value":"BEPK4U3I","created_at":"2026-07-05T03:49:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:BEPK4U3IKRZFYSNNMJDVTM3NNH","target":"record","payload":{"canonical_record":{"source":{"id":"2201.06923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2021-12-14T17:18:53Z","cross_cats_sorted":["cs.LG","gr-qc"],"title_canon_sha256":"46fd875250a358bf765b451e74b7dfe122513841184fd530bb1f9c0db6073ea1","abstract_canon_sha256":"14267747ad7ea2e57b5212889fda997e69819afc05021c257bbb358382d4ceb4"},"schema_version":"1.0"},"canonical_sha256":"091eae536854725c49ad624759b36d69fa638c0a61457bbe2f9ca3dbef9152a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:49:32.610699Z","signature_b64":"HnVpCGqVMNLo3CAIw99apDP+AyxjnrhMcS7UmnVh3/KCrSxF6foO2/6WnxUQFvhyzaCBjFlq2XQKxy1Qpsu4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"091eae536854725c49ad624759b36d69fa638c0a61457bbe2f9ca3dbef9152a4","last_reissued_at":"2026-07-05T03:49:32.610273Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:49:32.610273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.06923","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":"2026-07-05T03:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZjgHeFwQTlF8EDdC36I+BSMK7NVA86ziyyr2tv2MO2mOiKKNwQMhtAtgi04fXWyyvury07bsybiob5pGZxvYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:42:37.859636Z"},"content_sha256":"cc90f4cc15d48619988160bf478b1a95e180ee653ad25732f42a55c50801d050","schema_version":"1.0","event_id":"sha256:cc90f4cc15d48619988160bf478b1a95e180ee653ad25732f42a55c50801d050"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:BEPK4U3IKRZFYSNNMJDVTM3NNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Novel Approach to Topological Graph Theory with R-K Diagrams and Gravitational Wave Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","gr-qc"],"primary_cat":"astro-ph.HE","authors_text":"Andor Kesselman (Pathr.ai, Animikh Roy (University of Sussex, UK), USA)","submitted_at":"2021-12-14T17:18:53Z","abstract_excerpt":"Graph Theory and Topological Data Analytics, while powerful, have many drawbacks related to their sensitivity and consistency with TDA & Graph Network Analytics. In this paper, we aim to propose a novel approach for encoding vectorized associations between data points for the purpose of enabling smooth transitions between Graph and Topological Data Analytics. We conclusively reveal effective ways of converting such vectorized associations to simplicial complexes representing micro-states in a Phase-Space, resulting in filter specific, homotopic self-expressive, event-driven unique topological "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.06923","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/2201.06923/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":"2026-07-05T03:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCjKJOxNqD+Wp16u7X63WFb0+brotKKvyaLCZr05J5xSNyiqVpcYsiO5R29M7tYme+YZKw6sUd7MdDAfs83mCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:42:37.860396Z"},"content_sha256":"86c6dbc75eee38ab3ddfa03ad0bdc69f52d341743b4bc23af00a84ce8afbb315","schema_version":"1.0","event_id":"sha256:86c6dbc75eee38ab3ddfa03ad0bdc69f52d341743b4bc23af00a84ce8afbb315"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEPK4U3IKRZFYSNNMJDVTM3NNH/bundle.json","state_url":"https://pith.science/pith/BEPK4U3IKRZFYSNNMJDVTM3NNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEPK4U3IKRZFYSNNMJDVTM3NNH/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":"2026-08-12T09:42:37Z","links":{"resolver":"https://pith.science/pith/BEPK4U3IKRZFYSNNMJDVTM3NNH","bundle":"https://pith.science/pith/BEPK4U3IKRZFYSNNMJDVTM3NNH/bundle.json","state":"https://pith.science/pith/BEPK4U3IKRZFYSNNMJDVTM3NNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEPK4U3IKRZFYSNNMJDVTM3NNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BEPK4U3IKRZFYSNNMJDVTM3NNH","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":"14267747ad7ea2e57b5212889fda997e69819afc05021c257bbb358382d4ceb4","cross_cats_sorted":["cs.LG","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2021-12-14T17:18:53Z","title_canon_sha256":"46fd875250a358bf765b451e74b7dfe122513841184fd530bb1f9c0db6073ea1"},"schema_version":"1.0","source":{"id":"2201.06923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.06923","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"2201.06923v1","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.06923","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"BEPK4U3IKRZF","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"pith_short_16","alias_value":"BEPK4U3IKRZFYSNN","created_at":"2026-07-05T03:49:32Z"},{"alias_kind":"pith_short_8","alias_value":"BEPK4U3I","created_at":"2026-07-05T03:49:32Z"}],"graph_snapshots":[{"event_id":"sha256:86c6dbc75eee38ab3ddfa03ad0bdc69f52d341743b4bc23af00a84ce8afbb315","target":"graph","created_at":"2026-07-05T03:49:32Z","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/2201.06923/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph Theory and Topological Data Analytics, while powerful, have many drawbacks related to their sensitivity and consistency with TDA & Graph Network Analytics. In this paper, we aim to propose a novel approach for encoding vectorized associations between data points for the purpose of enabling smooth transitions between Graph and Topological Data Analytics. We conclusively reveal effective ways of converting such vectorized associations to simplicial complexes representing micro-states in a Phase-Space, resulting in filter specific, homotopic self-expressive, event-driven unique topological ","authors_text":"Andor Kesselman (Pathr.ai, Animikh Roy (University of Sussex, UK), USA)","cross_cats":["cs.LG","gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2021-12-14T17:18:53Z","title":"A Novel Approach to Topological Graph Theory with R-K Diagrams and Gravitational Wave Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.06923","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:cc90f4cc15d48619988160bf478b1a95e180ee653ad25732f42a55c50801d050","target":"record","created_at":"2026-07-05T03:49:32Z","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":"14267747ad7ea2e57b5212889fda997e69819afc05021c257bbb358382d4ceb4","cross_cats_sorted":["cs.LG","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2021-12-14T17:18:53Z","title_canon_sha256":"46fd875250a358bf765b451e74b7dfe122513841184fd530bb1f9c0db6073ea1"},"schema_version":"1.0","source":{"id":"2201.06923","kind":"arxiv","version":1}},"canonical_sha256":"091eae536854725c49ad624759b36d69fa638c0a61457bbe2f9ca3dbef9152a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"091eae536854725c49ad624759b36d69fa638c0a61457bbe2f9ca3dbef9152a4","first_computed_at":"2026-07-05T03:49:32.610273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:49:32.610273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HnVpCGqVMNLo3CAIw99apDP+AyxjnrhMcS7UmnVh3/KCrSxF6foO2/6WnxUQFvhyzaCBjFlq2XQKxy1Qpsu4Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:49:32.610699Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.06923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc90f4cc15d48619988160bf478b1a95e180ee653ad25732f42a55c50801d050","sha256:86c6dbc75eee38ab3ddfa03ad0bdc69f52d341743b4bc23af00a84ce8afbb315"],"state_sha256":"e56ab4830a2538d41225520730a2206427be90d864365567a78defa66dad3b9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNFChJXDR75TF8tGPPKHcqt3m2t/eA2r6B2+Gmps3KyEVwzSpZhUoX/rQ7SqS2x9l8U0khmlLQixCkUmi4IPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T09:42:37.870728Z","bundle_sha256":"6f0b00a9a633ea037183ae728ed3b225c3a067174be343597fcf8449b82255e6"}}