{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:UE2C3Q5FUWCIJJD7I7ZNETLO3Z","short_pith_number":"pith:UE2C3Q5F","canonical_record":{"source":{"id":"2206.00606","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-01T16:21:28Z","cross_cats_sorted":["cs.CV","cs.SI","math.AT","stat.ML"],"title_canon_sha256":"3d0c69966aabe60c29117c8bb04179bd47354bb1237d9904332dae541f7e1484","abstract_canon_sha256":"14638bd11fb9a2306f4fc722afb7379dcebc8651eaf9195302438d92551b4828"},"schema_version":"1.0"},"canonical_sha256":"a1342dc3a5a58484a47f47f2d24d6ede7ee44c6ab883bbd4d19e9a00ef18cea7","source":{"kind":"arxiv","id":"2206.00606","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.00606","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"2206.00606v3","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.00606","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"UE2C3Q5FUWCI","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"pith_short_16","alias_value":"UE2C3Q5FUWCIJJD7","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"pith_short_8","alias_value":"UE2C3Q5F","created_at":"2026-07-05T06:11:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:UE2C3Q5FUWCIJJD7I7ZNETLO3Z","target":"record","payload":{"canonical_record":{"source":{"id":"2206.00606","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-01T16:21:28Z","cross_cats_sorted":["cs.CV","cs.SI","math.AT","stat.ML"],"title_canon_sha256":"3d0c69966aabe60c29117c8bb04179bd47354bb1237d9904332dae541f7e1484","abstract_canon_sha256":"14638bd11fb9a2306f4fc722afb7379dcebc8651eaf9195302438d92551b4828"},"schema_version":"1.0"},"canonical_sha256":"a1342dc3a5a58484a47f47f2d24d6ede7ee44c6ab883bbd4d19e9a00ef18cea7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:55.663423Z","signature_b64":"hdmKX+6wHHQT0urAndUnDwAop6Q0/m1gOAW9d0i7QrYUmJfAX5DUZ3Vl/v+SOz0QOawN7H/VnahOVAgLMN4uBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1342dc3a5a58484a47f47f2d24d6ede7ee44c6ab883bbd4d19e9a00ef18cea7","last_reissued_at":"2026-07-05T06:11:55.662934Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:55.662934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.00606","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4E4ZIPBYKJ75hMIIU8QH6KxBQsUnH5+bu4eXtUcBCrJmFpCTxOQiJ3WTLYLwgF5szg0QNHRtn+Fv9ikjZ5NrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T05:46:19.657487Z"},"content_sha256":"f128ea21ed86734f94d2f7b24235fc451df465502cea64ed29f43209a75038c6","schema_version":"1.0","event_id":"sha256:f128ea21ed86734f94d2f7b24235fc451df465502cea64ed29f43209a75038c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:UE2C3Q5FUWCIJJD7I7ZNETLO3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Deep Learning: Going Beyond Graph Data","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.CV","cs.SI","math.AT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aldo Guzm\\'an-S\\'aenz, Ghada Zamzmi, Karthikeyan Natesan Ramamurthy, Michael T. Schaub, Mustafa Hajij, Neal Livesay, Nina Miolane, Paul Rosen, Robin Walters, Shreyas N. Samaga, Soham Mukherjee, Tamal K. Dey, Theodore Papamarkou, Tolga Birdal","submitted_at":"2022-06-01T16:21:28Z","abstract_excerpt":"Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains.\n  Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that mai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.00606","kind":"arxiv","version":3},"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/2206.00606/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":"2026-07-05T06:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+m6OeA7uinRVztwLJcFdI96RB04AXfJG8eo5s8EtygcSlMjCrlCwUNHM0PpprbHa00eQzY8GayagrH8VNQeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T05:46:19.657990Z"},"content_sha256":"2a19254bdbad45929c1995fd1f1293e5b6fe65758b4f533e564a1c79d7001dfd","schema_version":"1.0","event_id":"sha256:2a19254bdbad45929c1995fd1f1293e5b6fe65758b4f533e564a1c79d7001dfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UE2C3Q5FUWCIJJD7I7ZNETLO3Z/bundle.json","state_url":"https://pith.science/pith/UE2C3Q5FUWCIJJD7I7ZNETLO3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UE2C3Q5FUWCIJJD7I7ZNETLO3Z/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":"2026-08-08T05:46:19Z","links":{"resolver":"https://pith.science/pith/UE2C3Q5FUWCIJJD7I7ZNETLO3Z","bundle":"https://pith.science/pith/UE2C3Q5FUWCIJJD7I7ZNETLO3Z/bundle.json","state":"https://pith.science/pith/UE2C3Q5FUWCIJJD7I7ZNETLO3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UE2C3Q5FUWCIJJD7I7ZNETLO3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:UE2C3Q5FUWCIJJD7I7ZNETLO3Z","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":"14638bd11fb9a2306f4fc722afb7379dcebc8651eaf9195302438d92551b4828","cross_cats_sorted":["cs.CV","cs.SI","math.AT","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-01T16:21:28Z","title_canon_sha256":"3d0c69966aabe60c29117c8bb04179bd47354bb1237d9904332dae541f7e1484"},"schema_version":"1.0","source":{"id":"2206.00606","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.00606","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"2206.00606v3","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.00606","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"UE2C3Q5FUWCI","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"pith_short_16","alias_value":"UE2C3Q5FUWCIJJD7","created_at":"2026-07-05T06:11:55Z"},{"alias_kind":"pith_short_8","alias_value":"UE2C3Q5F","created_at":"2026-07-05T06:11:55Z"}],"graph_snapshots":[{"event_id":"sha256:2a19254bdbad45929c1995fd1f1293e5b6fe65758b4f533e564a1c79d7001dfd","target":"graph","created_at":"2026-07-05T06:11:55Z","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/2206.00606/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains.\n  Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that mai","authors_text":"Aldo Guzm\\'an-S\\'aenz, Ghada Zamzmi, Karthikeyan Natesan Ramamurthy, Michael T. Schaub, Mustafa Hajij, Neal Livesay, Nina Miolane, Paul Rosen, Robin Walters, Shreyas N. Samaga, Soham Mukherjee, Tamal K. Dey, Theodore Papamarkou, Tolga Birdal","cross_cats":["cs.CV","cs.SI","math.AT","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-01T16:21:28Z","title":"Topological Deep Learning: Going Beyond Graph Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.00606","kind":"arxiv","version":3},"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:f128ea21ed86734f94d2f7b24235fc451df465502cea64ed29f43209a75038c6","target":"record","created_at":"2026-07-05T06:11:55Z","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":"14638bd11fb9a2306f4fc722afb7379dcebc8651eaf9195302438d92551b4828","cross_cats_sorted":["cs.CV","cs.SI","math.AT","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-01T16:21:28Z","title_canon_sha256":"3d0c69966aabe60c29117c8bb04179bd47354bb1237d9904332dae541f7e1484"},"schema_version":"1.0","source":{"id":"2206.00606","kind":"arxiv","version":3}},"canonical_sha256":"a1342dc3a5a58484a47f47f2d24d6ede7ee44c6ab883bbd4d19e9a00ef18cea7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1342dc3a5a58484a47f47f2d24d6ede7ee44c6ab883bbd4d19e9a00ef18cea7","first_computed_at":"2026-07-05T06:11:55.662934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:11:55.662934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hdmKX+6wHHQT0urAndUnDwAop6Q0/m1gOAW9d0i7QrYUmJfAX5DUZ3Vl/v+SOz0QOawN7H/VnahOVAgLMN4uBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:11:55.663423Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.00606","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f128ea21ed86734f94d2f7b24235fc451df465502cea64ed29f43209a75038c6","sha256:2a19254bdbad45929c1995fd1f1293e5b6fe65758b4f533e564a1c79d7001dfd"],"state_sha256":"29237619b5a878945a3d262c4358c21fed150ab4a5fdfa6b83d0cba5ac6cb000"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zx9JzoCWh7zzRBv9MROD40UC2D6FeLO+p/AeniJohVNuamcBNgxhgS4y2v2mTPGVniBxcVvw7tjVMc1WG7dWCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T05:46:19.663052Z","bundle_sha256":"81500078bce42dc812dffc2a23b79dfe5774b62402cd68a9ebd0eaf6fe194fb0"}}