{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KCDYPYPQBKPQBN2KDLHUWUD5ZK","short_pith_number":"pith:KCDYPYPQ","canonical_record":{"source":{"id":"2605.23424","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-22T09:35:05Z","cross_cats_sorted":["cs.LG","math.IT"],"title_canon_sha256":"e2007f7f482f069be8ab6aaab688722a9a8c16a30b4405069eb6fc4c302c0df2","abstract_canon_sha256":"ba53f439cc71a0d29e76067bb2fbecede886098d1f09c06932ca09dfbe8e2e3d"},"schema_version":"1.0"},"canonical_sha256":"508787e1f00a9f00b74a1acf4b507dcaadfc1423737a695fbe1745147bc37d7c","source":{"kind":"arxiv","id":"2605.23424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23424","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23424v1","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23424","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"pith_short_12","alias_value":"KCDYPYPQBKPQ","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"pith_short_16","alias_value":"KCDYPYPQBKPQBN2K","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"pith_short_8","alias_value":"KCDYPYPQ","created_at":"2026-05-25T02:01:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KCDYPYPQBKPQBN2KDLHUWUD5ZK","target":"record","payload":{"canonical_record":{"source":{"id":"2605.23424","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-22T09:35:05Z","cross_cats_sorted":["cs.LG","math.IT"],"title_canon_sha256":"e2007f7f482f069be8ab6aaab688722a9a8c16a30b4405069eb6fc4c302c0df2","abstract_canon_sha256":"ba53f439cc71a0d29e76067bb2fbecede886098d1f09c06932ca09dfbe8e2e3d"},"schema_version":"1.0"},"canonical_sha256":"508787e1f00a9f00b74a1acf4b507dcaadfc1423737a695fbe1745147bc37d7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:53.723839Z","signature_b64":"Pl6f3ihrTtRWmjLYyFBQ3CPFfO2QH5uocM0GjJtll/MJn8w5DtDbQ4imPq5esG6raY2A9z/YbwgdrJ4Dzv1sBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"508787e1f00a9f00b74a1acf4b507dcaadfc1423737a695fbe1745147bc37d7c","last_reissued_at":"2026-05-25T02:01:53.723164Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:53.723164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.23424","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":"2026-05-25T02:01:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"My1ZY4qmC7DzRHqEj8YL8/b2bZm/I3xJSNVg8UaBpqloKNwqcvPJr8serWh+VxUYu/GqNub5+3CKXIYbwoemDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:40.854662Z"},"content_sha256":"9f494082d7070bb51866a51eba05576edd0e95ea8eb168dbe4d3fa5ec8b61772","schema_version":"1.0","event_id":"sha256:9f494082d7070bb51866a51eba05576edd0e95ea8eb168dbe4d3fa5ec8b61772"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KCDYPYPQBKPQBN2KDLHUWUD5ZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Mohammad Reza Deylam Salehi","submitted_at":"2026-05-22T09:35:05Z","abstract_excerpt":"In-network learning (INL) trains distributed neural modules by exchanging latent activations and backpropagated errors over a communication graph. This letter proposes Dijkstra-pruned INL (D-INL), which removes non-tree links by retaining a capacity-aware shortest-path tree rooted at the fusion node. To balance sparsity and predictive information, local routing (or aggregation) is modeled as a finite-rate stochastic gate with rate $R_g=I(Z; T)$. We derive a rate-distortion-generalization bound and validate the method on a reproducible distributed-classification experiment, where D-INL reduces "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23424","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/2605.23424/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":"2026-05-25T02:01:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UbzgunmZhVc98GRQPCKt4tENBANS7svMBHnxsSEXc342vKIcLFK0vyYZxwRIsr77RHZEvCWTRKC1z3K/7LpFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:40.855050Z"},"content_sha256":"47a41497bd25e44e61df15400951ddcc97070f8be147c78502de7ca6fcb0b22f","schema_version":"1.0","event_id":"sha256:47a41497bd25e44e61df15400951ddcc97070f8be147c78502de7ca6fcb0b22f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCDYPYPQBKPQBN2KDLHUWUD5ZK/bundle.json","state_url":"https://pith.science/pith/KCDYPYPQBKPQBN2KDLHUWUD5ZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCDYPYPQBKPQBN2KDLHUWUD5ZK/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":"2026-05-28T06:16:40Z","links":{"resolver":"https://pith.science/pith/KCDYPYPQBKPQBN2KDLHUWUD5ZK","bundle":"https://pith.science/pith/KCDYPYPQBKPQBN2KDLHUWUD5ZK/bundle.json","state":"https://pith.science/pith/KCDYPYPQBKPQBN2KDLHUWUD5ZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCDYPYPQBKPQBN2KDLHUWUD5ZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KCDYPYPQBKPQBN2KDLHUWUD5ZK","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":"ba53f439cc71a0d29e76067bb2fbecede886098d1f09c06932ca09dfbe8e2e3d","cross_cats_sorted":["cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-22T09:35:05Z","title_canon_sha256":"e2007f7f482f069be8ab6aaab688722a9a8c16a30b4405069eb6fc4c302c0df2"},"schema_version":"1.0","source":{"id":"2605.23424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23424","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23424v1","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23424","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"pith_short_12","alias_value":"KCDYPYPQBKPQ","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"pith_short_16","alias_value":"KCDYPYPQBKPQBN2K","created_at":"2026-05-25T02:01:53Z"},{"alias_kind":"pith_short_8","alias_value":"KCDYPYPQ","created_at":"2026-05-25T02:01:53Z"}],"graph_snapshots":[{"event_id":"sha256:47a41497bd25e44e61df15400951ddcc97070f8be147c78502de7ca6fcb0b22f","target":"graph","created_at":"2026-05-25T02:01:53Z","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/2605.23424/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In-network learning (INL) trains distributed neural modules by exchanging latent activations and backpropagated errors over a communication graph. This letter proposes Dijkstra-pruned INL (D-INL), which removes non-tree links by retaining a capacity-aware shortest-path tree rooted at the fusion node. To balance sparsity and predictive information, local routing (or aggregation) is modeled as a finite-rate stochastic gate with rate $R_g=I(Z; T)$. We derive a rate-distortion-generalization bound and validate the method on a reproducible distributed-classification experiment, where D-INL reduces ","authors_text":"Mohammad Reza Deylam Salehi","cross_cats":["cs.LG","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-22T09:35:05Z","title":"Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23424","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":"sha256:9f494082d7070bb51866a51eba05576edd0e95ea8eb168dbe4d3fa5ec8b61772","target":"record","created_at":"2026-05-25T02:01:53Z","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":"ba53f439cc71a0d29e76067bb2fbecede886098d1f09c06932ca09dfbe8e2e3d","cross_cats_sorted":["cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-22T09:35:05Z","title_canon_sha256":"e2007f7f482f069be8ab6aaab688722a9a8c16a30b4405069eb6fc4c302c0df2"},"schema_version":"1.0","source":{"id":"2605.23424","kind":"arxiv","version":1}},"canonical_sha256":"508787e1f00a9f00b74a1acf4b507dcaadfc1423737a695fbe1745147bc37d7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"508787e1f00a9f00b74a1acf4b507dcaadfc1423737a695fbe1745147bc37d7c","first_computed_at":"2026-05-25T02:01:53.723164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:53.723164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pl6f3ihrTtRWmjLYyFBQ3CPFfO2QH5uocM0GjJtll/MJn8w5DtDbQ4imPq5esG6raY2A9z/YbwgdrJ4Dzv1sBA==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:53.723839Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f494082d7070bb51866a51eba05576edd0e95ea8eb168dbe4d3fa5ec8b61772","sha256:47a41497bd25e44e61df15400951ddcc97070f8be147c78502de7ca6fcb0b22f"],"state_sha256":"7667c0e6de8a753b583ab711397bbc374d72c58181be90cc4d616905b5ddd5f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p7Bc/KH97wYAAlo6VOiG6h+0Qo9oxHdGbIpbEuvwvo4y2XjNoR9YSuBa4U4u15vagw/4i3mXD6R58fn5lDDAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:16:40.857251Z","bundle_sha256":"f1130fb75f94fece6bfc7cd3c57c3d23853a1557b7d2f0ecb543bf16f3c3f6c9"}}