{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3TFDKYLNBXOWNK4SYDRVPMOVTX","short_pith_number":"pith:3TFDKYLN","canonical_record":{"source":{"id":"2602.04675","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-04T15:48:09Z","cross_cats_sorted":[],"title_canon_sha256":"c0c5af19787ce2914bca04c077470069e0637698cb190b50c0aafd64baedb86c","abstract_canon_sha256":"77e22b85df2823e6968730fb79fe1383b21bcecb969c92b78f2292cb8ef4a219"},"schema_version":"1.0"},"canonical_sha256":"dcca35616d0ddd66ab92c0e357b1d59de38e69bf56b7c6463b642f385c052208","source":{"kind":"arxiv","id":"2602.04675","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.04675","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"2602.04675v2","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04675","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"3TFDKYLNBXOW","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"3TFDKYLNBXOWNK4S","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"3TFDKYLN","created_at":"2026-06-12T01:08:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3TFDKYLNBXOWNK4SYDRVPMOVTX","target":"record","payload":{"canonical_record":{"source":{"id":"2602.04675","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-04T15:48:09Z","cross_cats_sorted":[],"title_canon_sha256":"c0c5af19787ce2914bca04c077470069e0637698cb190b50c0aafd64baedb86c","abstract_canon_sha256":"77e22b85df2823e6968730fb79fe1383b21bcecb969c92b78f2292cb8ef4a219"},"schema_version":"1.0"},"canonical_sha256":"dcca35616d0ddd66ab92c0e357b1d59de38e69bf56b7c6463b642f385c052208","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:08:22.160298Z","signature_b64":"tbLFOLmWUlsRdDV40q/L1lJ7PggkWczo0maBAk95q98todO6p07GDA4bTEnHng/5irr3CA5DOo2eZLMtpzvmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcca35616d0ddd66ab92c0e357b1d59de38e69bf56b7c6463b642f385c052208","last_reissued_at":"2026-06-12T01:08:22.159113Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:08:22.159113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.04675","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":"2026-06-12T01:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LOnId54BeegOKE8ptbFQfMuYNiz9UD4K/6i4x4zJKx7QoaeGtVwGA9I19n2hiGDvPhmt+Xrck4AmtDZmP5L2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:13:21.722641Z"},"content_sha256":"67bb53d3876fa9aa7dad9e95ce5d2a036381418840c2e491412762ed29bb3e90","schema_version":"1.0","event_id":"sha256:67bb53d3876fa9aa7dad9e95ce5d2a036381418840c2e491412762ed29bb3e90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3TFDKYLNBXOWNK4SYDRVPMOVTX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Schr\\\"odinger Bridge on Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Evangelos Theodorou, Jaemoo Choi, Juno Nam, Panagiotis Theodoropoulos","submitted_at":"2026-02-04T15:48:09Z","abstract_excerpt":"Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this expressivity. They rely on restrictive assumptions, fail to generalize across sparse topologies, and scale poorly with graph size and time horizon. To address these issues, we introduce Generalized Schr\\\"odinger Bridge on Graphs (GSBoG), a novel scalable data-driven framework for learning executable controlled continuous-time Markov chain (CTMC) policies on arbitrary gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04675","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.04675/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":"2026-06-12T01:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3O5Ka/gVL8i5X2Fu8Vawm6XJhhA2JC+w9Xj3X/68qgEqzD4RuFivJkiwCL3MSt7SM0hy1WINiWvW3R8RS/YCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:13:21.723605Z"},"content_sha256":"27dacbc69f5e841367d8df3eb70e2f9bc70dab49e7987c944b6dd1b122e6e0fd","schema_version":"1.0","event_id":"sha256:27dacbc69f5e841367d8df3eb70e2f9bc70dab49e7987c944b6dd1b122e6e0fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TFDKYLNBXOWNK4SYDRVPMOVTX/bundle.json","state_url":"https://pith.science/pith/3TFDKYLNBXOWNK4SYDRVPMOVTX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TFDKYLNBXOWNK4SYDRVPMOVTX/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":"2026-08-09T06:13:21Z","links":{"resolver":"https://pith.science/pith/3TFDKYLNBXOWNK4SYDRVPMOVTX","bundle":"https://pith.science/pith/3TFDKYLNBXOWNK4SYDRVPMOVTX/bundle.json","state":"https://pith.science/pith/3TFDKYLNBXOWNK4SYDRVPMOVTX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TFDKYLNBXOWNK4SYDRVPMOVTX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3TFDKYLNBXOWNK4SYDRVPMOVTX","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":"77e22b85df2823e6968730fb79fe1383b21bcecb969c92b78f2292cb8ef4a219","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-04T15:48:09Z","title_canon_sha256":"c0c5af19787ce2914bca04c077470069e0637698cb190b50c0aafd64baedb86c"},"schema_version":"1.0","source":{"id":"2602.04675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.04675","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"2602.04675v2","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04675","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"3TFDKYLNBXOW","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"3TFDKYLNBXOWNK4S","created_at":"2026-06-12T01:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"3TFDKYLN","created_at":"2026-06-12T01:08:22Z"}],"graph_snapshots":[{"event_id":"sha256:27dacbc69f5e841367d8df3eb70e2f9bc70dab49e7987c944b6dd1b122e6e0fd","target":"graph","created_at":"2026-06-12T01:08:22Z","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/2602.04675/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this expressivity. They rely on restrictive assumptions, fail to generalize across sparse topologies, and scale poorly with graph size and time horizon. To address these issues, we introduce Generalized Schr\\\"odinger Bridge on Graphs (GSBoG), a novel scalable data-driven framework for learning executable controlled continuous-time Markov chain (CTMC) policies on arbitrary gr","authors_text":"Evangelos Theodorou, Jaemoo Choi, Juno Nam, Panagiotis Theodoropoulos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-04T15:48:09Z","title":"Generalized Schr\\\"odinger Bridge on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04675","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":"sha256:67bb53d3876fa9aa7dad9e95ce5d2a036381418840c2e491412762ed29bb3e90","target":"record","created_at":"2026-06-12T01:08:22Z","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":"77e22b85df2823e6968730fb79fe1383b21bcecb969c92b78f2292cb8ef4a219","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-04T15:48:09Z","title_canon_sha256":"c0c5af19787ce2914bca04c077470069e0637698cb190b50c0aafd64baedb86c"},"schema_version":"1.0","source":{"id":"2602.04675","kind":"arxiv","version":2}},"canonical_sha256":"dcca35616d0ddd66ab92c0e357b1d59de38e69bf56b7c6463b642f385c052208","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcca35616d0ddd66ab92c0e357b1d59de38e69bf56b7c6463b642f385c052208","first_computed_at":"2026-06-12T01:08:22.159113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:08:22.159113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tbLFOLmWUlsRdDV40q/L1lJ7PggkWczo0maBAk95q98todO6p07GDA4bTEnHng/5irr3CA5DOo2eZLMtpzvmBA==","signature_status":"signed_v1","signed_at":"2026-06-12T01:08:22.160298Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.04675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67bb53d3876fa9aa7dad9e95ce5d2a036381418840c2e491412762ed29bb3e90","sha256:27dacbc69f5e841367d8df3eb70e2f9bc70dab49e7987c944b6dd1b122e6e0fd"],"state_sha256":"8be5bdefba1b815376fb844d26f3ba9dd8d7baedc3b11275b2b2bb6039c7594e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kbo4szAgPx1GSJg8HchRHc7SYiYma4fJgwcLMPuUREHmt8/t9BMUyOsqaigfNq3Tmau1gjo21go5rCDb78WYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:13:21.729886Z","bundle_sha256":"5ebe7d62cb0d1b2258ce6aa79b42189ab4f0c3e191657b113b85813c1da2cc5a"}}