{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JJM7S3CBOUNN5XBZZPGITBIDM3","short_pith_number":"pith:JJM7S3CB","canonical_record":{"source":{"id":"2606.27432","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-06-25T18:00:10Z","cross_cats_sorted":["math.DG","stat.AP"],"title_canon_sha256":"f8c6b2192eca81482414078a29327bb397b06be3ff7b473d661699b896462898","abstract_canon_sha256":"ad327a3a8d77f59b9207cf7bbe8c191b149da101d1a0222fc1ec7f9348f1c379"},"schema_version":"1.0"},"canonical_sha256":"4a59f96c41751adedc39cbcc89850366d6758b096f612b71834cc1c1f488e4ac","source":{"kind":"arxiv","id":"2606.27432","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27432","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27432v1","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27432","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"pith_short_12","alias_value":"JJM7S3CBOUNN","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"pith_short_16","alias_value":"JJM7S3CBOUNN5XBZ","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"pith_short_8","alias_value":"JJM7S3CB","created_at":"2026-06-29T00:14:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JJM7S3CBOUNN5XBZZPGITBIDM3","target":"record","payload":{"canonical_record":{"source":{"id":"2606.27432","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-06-25T18:00:10Z","cross_cats_sorted":["math.DG","stat.AP"],"title_canon_sha256":"f8c6b2192eca81482414078a29327bb397b06be3ff7b473d661699b896462898","abstract_canon_sha256":"ad327a3a8d77f59b9207cf7bbe8c191b149da101d1a0222fc1ec7f9348f1c379"},"schema_version":"1.0"},"canonical_sha256":"4a59f96c41751adedc39cbcc89850366d6758b096f612b71834cc1c1f488e4ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T00:14:05.926243Z","signature_b64":"LDXrtawlrHpSJvXsiONQoR7N5xXPUdt7kHqt08UhzoHfExmUekJUBa0u5jtovszNBUXVG/mC55CigRfquNy+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a59f96c41751adedc39cbcc89850366d6758b096f612b71834cc1c1f488e4ac","last_reissued_at":"2026-06-29T00:14:05.925833Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T00:14:05.925833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.27432","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":"2026-06-29T00:14:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tRLXlfR9Kry//sVi9MROEraOWCrwDgz/ottSUY6OrRKMq/zT7DGgeLKBjgLpLwTcn+JerPjKsRLawwi2FR1WDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:07:45.542789Z"},"content_sha256":"f18e0565ec240857bac85b779df6090783caf7d7730b085827410a78d40473f7","schema_version":"1.0","event_id":"sha256:f18e0565ec240857bac85b779df6090783caf7d7730b085827410a78d40473f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JJM7S3CBOUNN5XBZZPGITBIDM3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hidden Geometry of Astrophysical Spectra: Path-Signatures of Line Profiles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","stat.AP"],"primary_cat":"astro-ph.IM","authors_text":"Rafael S. de Souza, Severin Bunk","submitted_at":"2026-06-25T18:00:10Z","abstract_excerpt":"The morphology of a spectral-line profile contains information beyond scalar summaries of line strength, centroid, width, global asymmetry, or diagnostic line ratios. Broad wings, shoulders, double peaks, secondary components, and composite emission--absorption structures encode how flux is ordered across wavelength but can remain indistinguishable under conventional summaries. We introduce an interpretable geometric representation of line profiles inspired by rough path theory. Each wavelength-sampled profile is mapped to a common systemic rest-frame velocity grid and treated as a trajectory "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27432","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/2606.27432/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":"2026-06-29T00:14:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wzXg863m0dmDryqedR31PjeNZHvl+bbmz2682AETi6vViUTQeCO28pprko+9MXbr7nE+bEclLgY/yT4nTBbMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:07:45.543154Z"},"content_sha256":"1d40fe5da0515f60bfb1c1fe5f4d0355bfbe0c51db21f01a092e6344ed1d7d66","schema_version":"1.0","event_id":"sha256:1d40fe5da0515f60bfb1c1fe5f4d0355bfbe0c51db21f01a092e6344ed1d7d66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJM7S3CBOUNN5XBZZPGITBIDM3/bundle.json","state_url":"https://pith.science/pith/JJM7S3CBOUNN5XBZZPGITBIDM3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJM7S3CBOUNN5XBZZPGITBIDM3/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":"2026-06-29T13:07:45Z","links":{"resolver":"https://pith.science/pith/JJM7S3CBOUNN5XBZZPGITBIDM3","bundle":"https://pith.science/pith/JJM7S3CBOUNN5XBZZPGITBIDM3/bundle.json","state":"https://pith.science/pith/JJM7S3CBOUNN5XBZZPGITBIDM3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJM7S3CBOUNN5XBZZPGITBIDM3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JJM7S3CBOUNN5XBZZPGITBIDM3","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":"ad327a3a8d77f59b9207cf7bbe8c191b149da101d1a0222fc1ec7f9348f1c379","cross_cats_sorted":["math.DG","stat.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-06-25T18:00:10Z","title_canon_sha256":"f8c6b2192eca81482414078a29327bb397b06be3ff7b473d661699b896462898"},"schema_version":"1.0","source":{"id":"2606.27432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27432","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27432v1","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27432","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"pith_short_12","alias_value":"JJM7S3CBOUNN","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"pith_short_16","alias_value":"JJM7S3CBOUNN5XBZ","created_at":"2026-06-29T00:14:05Z"},{"alias_kind":"pith_short_8","alias_value":"JJM7S3CB","created_at":"2026-06-29T00:14:05Z"}],"graph_snapshots":[{"event_id":"sha256:1d40fe5da0515f60bfb1c1fe5f4d0355bfbe0c51db21f01a092e6344ed1d7d66","target":"graph","created_at":"2026-06-29T00:14:05Z","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/2606.27432/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The morphology of a spectral-line profile contains information beyond scalar summaries of line strength, centroid, width, global asymmetry, or diagnostic line ratios. Broad wings, shoulders, double peaks, secondary components, and composite emission--absorption structures encode how flux is ordered across wavelength but can remain indistinguishable under conventional summaries. We introduce an interpretable geometric representation of line profiles inspired by rough path theory. Each wavelength-sampled profile is mapped to a common systemic rest-frame velocity grid and treated as a trajectory ","authors_text":"Rafael S. de Souza, Severin Bunk","cross_cats":["math.DG","stat.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-06-25T18:00:10Z","title":"The Hidden Geometry of Astrophysical Spectra: Path-Signatures of Line Profiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27432","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:f18e0565ec240857bac85b779df6090783caf7d7730b085827410a78d40473f7","target":"record","created_at":"2026-06-29T00:14:05Z","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":"ad327a3a8d77f59b9207cf7bbe8c191b149da101d1a0222fc1ec7f9348f1c379","cross_cats_sorted":["math.DG","stat.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-06-25T18:00:10Z","title_canon_sha256":"f8c6b2192eca81482414078a29327bb397b06be3ff7b473d661699b896462898"},"schema_version":"1.0","source":{"id":"2606.27432","kind":"arxiv","version":1}},"canonical_sha256":"4a59f96c41751adedc39cbcc89850366d6758b096f612b71834cc1c1f488e4ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a59f96c41751adedc39cbcc89850366d6758b096f612b71834cc1c1f488e4ac","first_computed_at":"2026-06-29T00:14:05.925833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T00:14:05.925833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDXrtawlrHpSJvXsiONQoR7N5xXPUdt7kHqt08UhzoHfExmUekJUBa0u5jtovszNBUXVG/mC55CigRfquNy+BQ==","signature_status":"signed_v1","signed_at":"2026-06-29T00:14:05.926243Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f18e0565ec240857bac85b779df6090783caf7d7730b085827410a78d40473f7","sha256:1d40fe5da0515f60bfb1c1fe5f4d0355bfbe0c51db21f01a092e6344ed1d7d66"],"state_sha256":"967251943e175c09ee203136dcde858f580c8144d79c5095fcdb02fe2c5e51ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X5+eMr4GeyFDhOkM+7kaRgX7kzAnQBVTCV7ElkGvJlHtvwXKutqdejZ/4j+By67eFRjCqOr07LVMtCkuh9yDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T13:07:45.545102Z","bundle_sha256":"64b9f624fa42466d8dd3edecf60ae19e3301d8a97c1ee71d01d242f3e3b2fd52"}}