{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AAA4LQBY7UGPPQFCBKFQET7OCM","short_pith_number":"pith:AAA4LQBY","canonical_record":{"source":{"id":"1209.2295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-09-11T12:01:08Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"ba2f8973f9cc6e0cc3331aa1ed65524b15e837d0e70f4fecbb31bd4b3fbceb88","abstract_canon_sha256":"1039b3038dfc2ca6f45504cff2de3723319d9c524998165479f82bb6d8b46675"},"schema_version":"1.0"},"canonical_sha256":"0001c5c038fd0cf7c0a20a8b024fee1314b0d738af5b5bd111b1ff4c25270f8b","source":{"kind":"arxiv","id":"1209.2295","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2295","created_at":"2026-05-18T03:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2295v2","created_at":"2026-05-18T03:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2295","created_at":"2026-05-18T03:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"AAA4LQBY7UGP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AAA4LQBY7UGPPQFC","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AAA4LQBY","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AAA4LQBY7UGPPQFCBKFQET7OCM","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-09-11T12:01:08Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"ba2f8973f9cc6e0cc3331aa1ed65524b15e837d0e70f4fecbb31bd4b3fbceb88","abstract_canon_sha256":"1039b3038dfc2ca6f45504cff2de3723319d9c524998165479f82bb6d8b46675"},"schema_version":"1.0"},"canonical_sha256":"0001c5c038fd0cf7c0a20a8b024fee1314b0d738af5b5bd111b1ff4c25270f8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:43.231732Z","signature_b64":"Nr1Ee0SIdjn7jk1xC+e7nzllOh3rh0IFxNhoAqv9J5Ma5RScppOn/hvak7CUDQ2a/mRdLkvKJFy0H3yAa3FfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0001c5c038fd0cf7c0a20a8b024fee1314b0d738af5b5bd111b1ff4c25270f8b","last_reissued_at":"2026-05-18T03:45:43.231004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:43.231004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2295","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ECH0/0efET8CiYBHQeRIop73JfBDgY11G+NO/f22US1yC2yLcyC26xCcS5IcBCukwxqhsmoDFQrJ6P+p4xe5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:08:59.560067Z"},"content_sha256":"e67201674e99583c252b82e5af3fe7727a63dd65d4d6e91ff4986dd918483c02","schema_version":"1.0","event_id":"sha256:e67201674e99583c252b82e5af3fe7727a63dd65d4d6e91ff4986dd918483c02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AAA4LQBY7UGPPQFCBKFQET7OCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multimodal diffusion geometry by joint diagonalization of Laplacians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.CV","authors_text":"Alexander M. Bronstein, Davide Eynard, Klaus Glashoff, Michael M. Bronstein","submitted_at":"2012-09-11T12:01:08Z","abstract_excerpt":"We construct an extension of diffusion geometry to multiple modalities through joint approximate diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, retrieval, and clustering demonstrating that the joint diffusion geometry frequently better captures the inherent structure of multi-modal data. We also show that many previous attempts to construct multimodal spectral clustering can be seen as particular cases of j"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2295","kind":"arxiv","version":2},"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":"2026-05-18T03:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+79Hubw4/idWMoB+JoirikZD33F/jSfyDGKxNMuw6LwnFCiEsqhQWq+LYI2F4F2RAcMgXCSczWw3Y6SaQY8aAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:08:59.560759Z"},"content_sha256":"dfa3b97a8ceaf0e01fe38d9659593b9f4f13593fdf43ca3059de4a895f9a81e3","schema_version":"1.0","event_id":"sha256:dfa3b97a8ceaf0e01fe38d9659593b9f4f13593fdf43ca3059de4a895f9a81e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AAA4LQBY7UGPPQFCBKFQET7OCM/bundle.json","state_url":"https://pith.science/pith/AAA4LQBY7UGPPQFCBKFQET7OCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AAA4LQBY7UGPPQFCBKFQET7OCM/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":"2026-05-25T20:08:59Z","links":{"resolver":"https://pith.science/pith/AAA4LQBY7UGPPQFCBKFQET7OCM","bundle":"https://pith.science/pith/AAA4LQBY7UGPPQFCBKFQET7OCM/bundle.json","state":"https://pith.science/pith/AAA4LQBY7UGPPQFCBKFQET7OCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AAA4LQBY7UGPPQFCBKFQET7OCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AAA4LQBY7UGPPQFCBKFQET7OCM","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":"1039b3038dfc2ca6f45504cff2de3723319d9c524998165479f82bb6d8b46675","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-09-11T12:01:08Z","title_canon_sha256":"ba2f8973f9cc6e0cc3331aa1ed65524b15e837d0e70f4fecbb31bd4b3fbceb88"},"schema_version":"1.0","source":{"id":"1209.2295","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2295","created_at":"2026-05-18T03:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2295v2","created_at":"2026-05-18T03:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2295","created_at":"2026-05-18T03:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"AAA4LQBY7UGP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AAA4LQBY7UGPPQFC","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AAA4LQBY","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:dfa3b97a8ceaf0e01fe38d9659593b9f4f13593fdf43ca3059de4a895f9a81e3","target":"graph","created_at":"2026-05-18T03:45:43Z","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":"We construct an extension of diffusion geometry to multiple modalities through joint approximate diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, retrieval, and clustering demonstrating that the joint diffusion geometry frequently better captures the inherent structure of multi-modal data. We also show that many previous attempts to construct multimodal spectral clustering can be seen as particular cases of j","authors_text":"Alexander M. Bronstein, Davide Eynard, Klaus Glashoff, Michael M. Bronstein","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-09-11T12:01:08Z","title":"Multimodal diffusion geometry by joint diagonalization of Laplacians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2295","kind":"arxiv","version":2},"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:e67201674e99583c252b82e5af3fe7727a63dd65d4d6e91ff4986dd918483c02","target":"record","created_at":"2026-05-18T03:45:43Z","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":"1039b3038dfc2ca6f45504cff2de3723319d9c524998165479f82bb6d8b46675","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-09-11T12:01:08Z","title_canon_sha256":"ba2f8973f9cc6e0cc3331aa1ed65524b15e837d0e70f4fecbb31bd4b3fbceb88"},"schema_version":"1.0","source":{"id":"1209.2295","kind":"arxiv","version":2}},"canonical_sha256":"0001c5c038fd0cf7c0a20a8b024fee1314b0d738af5b5bd111b1ff4c25270f8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0001c5c038fd0cf7c0a20a8b024fee1314b0d738af5b5bd111b1ff4c25270f8b","first_computed_at":"2026-05-18T03:45:43.231004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:43.231004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nr1Ee0SIdjn7jk1xC+e7nzllOh3rh0IFxNhoAqv9J5Ma5RScppOn/hvak7CUDQ2a/mRdLkvKJFy0H3yAa3FfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:43.231732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2295","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e67201674e99583c252b82e5af3fe7727a63dd65d4d6e91ff4986dd918483c02","sha256:dfa3b97a8ceaf0e01fe38d9659593b9f4f13593fdf43ca3059de4a895f9a81e3"],"state_sha256":"4a0057d9a0673939ea199c4ef9f28aa338264eac4be233b3295117f68d8a594c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4O9gEuUqrVHW3qLIj9KrmY+483v7YMIbtcevaELDT0mceniAy7GBvJnkPBC0ESXcRMQW6o9ftvWEx94I/86MBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:08:59.564499Z","bundle_sha256":"e7da4da9f8053f81f25c1eddda77414b38566975cd7c98c39723f2bce5b20af8"}}