{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ABLEGM22OFRTK7LYRHID4RPOMM","short_pith_number":"pith:ABLEGM22","canonical_record":{"source":{"id":"2406.04102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2024-06-06T14:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"973bed14f5a70ba1ba387e0dff514e3137080d0f0a1927754c68ce843770c775","abstract_canon_sha256":"5581153f8e9889d1e6120c81670172433e4bfa89362aa923a0b16cd51f4e51c8"},"schema_version":"1.0"},"canonical_sha256":"005643335a7163357d7889d03e45ee632b46b2177ec247ee45971ee981a500fc","source":{"kind":"arxiv","id":"2406.04102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.04102","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.04102v1","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.04102","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"ABLEGM22OFRT","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"pith_short_16","alias_value":"ABLEGM22OFRTK7LY","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"pith_short_8","alias_value":"ABLEGM22","created_at":"2026-07-05T08:28:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ABLEGM22OFRTK7LYRHID4RPOMM","target":"record","payload":{"canonical_record":{"source":{"id":"2406.04102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2024-06-06T14:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"973bed14f5a70ba1ba387e0dff514e3137080d0f0a1927754c68ce843770c775","abstract_canon_sha256":"5581153f8e9889d1e6120c81670172433e4bfa89362aa923a0b16cd51f4e51c8"},"schema_version":"1.0"},"canonical_sha256":"005643335a7163357d7889d03e45ee632b46b2177ec247ee45971ee981a500fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:28:20.754724Z","signature_b64":"NsxgXrC4C59Y4y6mpKi0Jf21rwlgXoMcR7ibelfRpkcQLFK7JJ/knED/dtlpqe60NNDbCvi2i/so1sTe60krBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"005643335a7163357d7889d03e45ee632b46b2177ec247ee45971ee981a500fc","last_reissued_at":"2026-07-05T08:28:20.754248Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:28:20.754248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.04102","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":"2026-07-05T08:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kYdiZRsEFbdHRZVZKfWU95c7i4kg38KgqJ/LvsJ/u8GEirZJQQcjffLVA54XoTMrQZPqiygr3p4aqkG4zPhPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:07:46.858839Z"},"content_sha256":"0d64142472ce2c871d49912f94006388b01e08efab4fe2f3ca966d107d908ff6","schema_version":"1.0","event_id":"sha256:0d64142472ce2c871d49912f94006388b01e08efab4fe2f3ca966d107d908ff6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ABLEGM22OFRTK7LYRHID4RPOMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chromatic Topological Data Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Herbert Edelsbrunner, Morteza Saghafian, Ondrej Draganov, Sebastiano Cultrera di Montesano","submitted_at":"2024-06-06T14:17:50Z","abstract_excerpt":"Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial interactions among multiple configurations, each distinguished by a color. It describes advances in this area and prepares the ground for further exploration by mentioning unresolved questions and promising research avenues while focusing on the overlap with discrete geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.04102","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/2406.04102/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":"2026-07-05T08:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvBZmBzAgzhfrXYdNa+3FPi+orpfloNH2AwxUaNWOXBTiI3HSQEH5yMKo7Md8aiVAdLVjzVEuYLj2oDu+Qb0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:07:46.859641Z"},"content_sha256":"bf60fdae4a8f2e38ed6192e79d474c355282456bd3752878c470eb50e19613c8","schema_version":"1.0","event_id":"sha256:bf60fdae4a8f2e38ed6192e79d474c355282456bd3752878c470eb50e19613c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABLEGM22OFRTK7LYRHID4RPOMM/bundle.json","state_url":"https://pith.science/pith/ABLEGM22OFRTK7LYRHID4RPOMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABLEGM22OFRTK7LYRHID4RPOMM/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":"2026-08-11T22:07:46Z","links":{"resolver":"https://pith.science/pith/ABLEGM22OFRTK7LYRHID4RPOMM","bundle":"https://pith.science/pith/ABLEGM22OFRTK7LYRHID4RPOMM/bundle.json","state":"https://pith.science/pith/ABLEGM22OFRTK7LYRHID4RPOMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABLEGM22OFRTK7LYRHID4RPOMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ABLEGM22OFRTK7LYRHID4RPOMM","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":"5581153f8e9889d1e6120c81670172433e4bfa89362aa923a0b16cd51f4e51c8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2024-06-06T14:17:50Z","title_canon_sha256":"973bed14f5a70ba1ba387e0dff514e3137080d0f0a1927754c68ce843770c775"},"schema_version":"1.0","source":{"id":"2406.04102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.04102","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.04102v1","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.04102","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"ABLEGM22OFRT","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"pith_short_16","alias_value":"ABLEGM22OFRTK7LY","created_at":"2026-07-05T08:28:20Z"},{"alias_kind":"pith_short_8","alias_value":"ABLEGM22","created_at":"2026-07-05T08:28:20Z"}],"graph_snapshots":[{"event_id":"sha256:bf60fdae4a8f2e38ed6192e79d474c355282456bd3752878c470eb50e19613c8","target":"graph","created_at":"2026-07-05T08:28:20Z","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/2406.04102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial interactions among multiple configurations, each distinguished by a color. It describes advances in this area and prepares the ground for further exploration by mentioning unresolved questions and promising research avenues while focusing on the overlap with discrete geometry.","authors_text":"Herbert Edelsbrunner, Morteza Saghafian, Ondrej Draganov, Sebastiano Cultrera di Montesano","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2024-06-06T14:17:50Z","title":"Chromatic Topological Data Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.04102","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":"sha256:0d64142472ce2c871d49912f94006388b01e08efab4fe2f3ca966d107d908ff6","target":"record","created_at":"2026-07-05T08:28:20Z","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":"5581153f8e9889d1e6120c81670172433e4bfa89362aa923a0b16cd51f4e51c8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2024-06-06T14:17:50Z","title_canon_sha256":"973bed14f5a70ba1ba387e0dff514e3137080d0f0a1927754c68ce843770c775"},"schema_version":"1.0","source":{"id":"2406.04102","kind":"arxiv","version":1}},"canonical_sha256":"005643335a7163357d7889d03e45ee632b46b2177ec247ee45971ee981a500fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"005643335a7163357d7889d03e45ee632b46b2177ec247ee45971ee981a500fc","first_computed_at":"2026-07-05T08:28:20.754248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:28:20.754248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NsxgXrC4C59Y4y6mpKi0Jf21rwlgXoMcR7ibelfRpkcQLFK7JJ/knED/dtlpqe60NNDbCvi2i/so1sTe60krBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:28:20.754724Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.04102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d64142472ce2c871d49912f94006388b01e08efab4fe2f3ca966d107d908ff6","sha256:bf60fdae4a8f2e38ed6192e79d474c355282456bd3752878c470eb50e19613c8"],"state_sha256":"2de025cadc1286513fd8b9caa9246c913694c1f5fa1ee9b29c798765a03516a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WsbHT54iftO4d18Uh17MwQz9dJH6jsA5SxhokF3tg/UERAuM7l+nrfc+gRjPtchsOuMKCOLSFwBxIwwpm5hjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T22:07:46.865019Z","bundle_sha256":"41fbd3b0038e1aff0752b8f2c094eb68327c9f9acb02b47ed5d7193c5108e9f0"}}