{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:T75SQKKCVVDGLMK6TP3U7LEB6F","short_pith_number":"pith:T75SQKKC","canonical_record":{"source":{"id":"2312.04928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-08T09:44:28Z","cross_cats_sorted":[],"title_canon_sha256":"07a97bcf4f40424ab10ddb3e26388fd1e07d573dc8bd871e303a156db585b71c","abstract_canon_sha256":"ad46d335f9ba4079d36946d8103ac365be212b5ada3ba2725e5dee40b1d7a665"},"schema_version":"1.0"},"canonical_sha256":"9ffb282942ad4665b15e9bf74fac81f167db308705b13b23c5db2eeecbc603e8","source":{"kind":"arxiv","id":"2312.04928","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04928","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04928v2","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04928","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"T75SQKKCVVDG","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"pith_short_16","alias_value":"T75SQKKCVVDGLMK6","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"pith_short_8","alias_value":"T75SQKKC","created_at":"2026-07-05T08:12:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:T75SQKKCVVDGLMK6TP3U7LEB6F","target":"record","payload":{"canonical_record":{"source":{"id":"2312.04928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-08T09:44:28Z","cross_cats_sorted":[],"title_canon_sha256":"07a97bcf4f40424ab10ddb3e26388fd1e07d573dc8bd871e303a156db585b71c","abstract_canon_sha256":"ad46d335f9ba4079d36946d8103ac365be212b5ada3ba2725e5dee40b1d7a665"},"schema_version":"1.0"},"canonical_sha256":"9ffb282942ad4665b15e9bf74fac81f167db308705b13b23c5db2eeecbc603e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:12:46.773893Z","signature_b64":"51lIcWUa314AOjar3g39VNqGLAoD2502qQcpaZPjRX14IT0pzoR0t2r6SR/4aQELfBxSjJhdg80gt+LD4e5+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ffb282942ad4665b15e9bf74fac81f167db308705b13b23c5db2eeecbc603e8","last_reissued_at":"2026-07-05T08:12:46.773448Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:12:46.773448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.04928","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":"2026-07-05T08:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rfTybNgJqugX/Rh5Yt4Xpskno3JeovCCh4xn0512ethdEsKni7ImaLClLfvA8hRXiTq3Jc9XJge2pAVjMP1/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:11:25.201104Z"},"content_sha256":"8bb4c49f9cc1d52a919f160676d3a88c31498046fe014a4bf1f747fd0b2920d7","schema_version":"1.0","event_id":"sha256:8bb4c49f9cc1d52a919f160676d3a88c31498046fe014a4bf1f747fd0b2920d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:T75SQKKCVVDGLMK6TP3U7LEB6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding the Influence of Digraphs on Decentralized Optimization: Effective Metrics, Lower Bound, and Optimal Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kun Yuan, Liyuan Liang, Ran Xin, Xinmeng Huang","submitted_at":"2023-12-08T09:44:28Z","abstract_excerpt":"This paper investigates the influence of directed networks on decentralized stochastic non-convex optimization associated with column-stochastic mixing matrices. Surprisingly, we find that the canonical spectral gap, a widely used metric in undirected networks, is insufficient to characterize the impact of directed topology on decentralized algorithms. To overcome this limitation, we introduce a novel metric termed equilibrium skewness. This metric, together with the spectral gap, accurately and comprehensively captures the influence of column-stochastic mixing matrices on decentralized stocha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04928","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/2312.04928/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":"2026-07-05T08:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zwVHM8wozo5z7dCeJpn5IStH4W+4r0N3CUWCf08axmPYhD/T0fWoORxwEnvOjptDIMK0641dkbUK/K9McRnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:11:25.201625Z"},"content_sha256":"8a6a745ab4d31c47706eb841ab2c5e7fca0dd9f04382091e1c48b3b3732af2f3","schema_version":"1.0","event_id":"sha256:8a6a745ab4d31c47706eb841ab2c5e7fca0dd9f04382091e1c48b3b3732af2f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T75SQKKCVVDGLMK6TP3U7LEB6F/bundle.json","state_url":"https://pith.science/pith/T75SQKKCVVDGLMK6TP3U7LEB6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T75SQKKCVVDGLMK6TP3U7LEB6F/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":"2026-08-08T10:11:25Z","links":{"resolver":"https://pith.science/pith/T75SQKKCVVDGLMK6TP3U7LEB6F","bundle":"https://pith.science/pith/T75SQKKCVVDGLMK6TP3U7LEB6F/bundle.json","state":"https://pith.science/pith/T75SQKKCVVDGLMK6TP3U7LEB6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T75SQKKCVVDGLMK6TP3U7LEB6F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:T75SQKKCVVDGLMK6TP3U7LEB6F","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":"ad46d335f9ba4079d36946d8103ac365be212b5ada3ba2725e5dee40b1d7a665","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-08T09:44:28Z","title_canon_sha256":"07a97bcf4f40424ab10ddb3e26388fd1e07d573dc8bd871e303a156db585b71c"},"schema_version":"1.0","source":{"id":"2312.04928","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04928","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04928v2","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04928","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"T75SQKKCVVDG","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"pith_short_16","alias_value":"T75SQKKCVVDGLMK6","created_at":"2026-07-05T08:12:46Z"},{"alias_kind":"pith_short_8","alias_value":"T75SQKKC","created_at":"2026-07-05T08:12:46Z"}],"graph_snapshots":[{"event_id":"sha256:8a6a745ab4d31c47706eb841ab2c5e7fca0dd9f04382091e1c48b3b3732af2f3","target":"graph","created_at":"2026-07-05T08:12:46Z","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/2312.04928/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the influence of directed networks on decentralized stochastic non-convex optimization associated with column-stochastic mixing matrices. Surprisingly, we find that the canonical spectral gap, a widely used metric in undirected networks, is insufficient to characterize the impact of directed topology on decentralized algorithms. To overcome this limitation, we introduce a novel metric termed equilibrium skewness. This metric, together with the spectral gap, accurately and comprehensively captures the influence of column-stochastic mixing matrices on decentralized stocha","authors_text":"Kun Yuan, Liyuan Liang, Ran Xin, Xinmeng Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-08T09:44:28Z","title":"Understanding the Influence of Digraphs on Decentralized Optimization: Effective Metrics, Lower Bound, and Optimal Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04928","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":"sha256:8bb4c49f9cc1d52a919f160676d3a88c31498046fe014a4bf1f747fd0b2920d7","target":"record","created_at":"2026-07-05T08:12:46Z","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":"ad46d335f9ba4079d36946d8103ac365be212b5ada3ba2725e5dee40b1d7a665","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-08T09:44:28Z","title_canon_sha256":"07a97bcf4f40424ab10ddb3e26388fd1e07d573dc8bd871e303a156db585b71c"},"schema_version":"1.0","source":{"id":"2312.04928","kind":"arxiv","version":2}},"canonical_sha256":"9ffb282942ad4665b15e9bf74fac81f167db308705b13b23c5db2eeecbc603e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ffb282942ad4665b15e9bf74fac81f167db308705b13b23c5db2eeecbc603e8","first_computed_at":"2026-07-05T08:12:46.773448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:12:46.773448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"51lIcWUa314AOjar3g39VNqGLAoD2502qQcpaZPjRX14IT0pzoR0t2r6SR/4aQELfBxSjJhdg80gt+LD4e5+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:12:46.773893Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.04928","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bb4c49f9cc1d52a919f160676d3a88c31498046fe014a4bf1f747fd0b2920d7","sha256:8a6a745ab4d31c47706eb841ab2c5e7fca0dd9f04382091e1c48b3b3732af2f3"],"state_sha256":"5b88a3cb84d0e7dea77dda982c8a7f27866b00fedd6b5d1f113e9111a97ea7a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fq07s6Nt9l1psJ1Knf7Tf3asFVBqzayaF8fItlp3khniT5k7F4snV4mmkXYjvXCEDp8lSm1STj+wmJEouCGTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T10:11:25.206210Z","bundle_sha256":"714a4cedd8ccce07e476192e14aaa040b4282ea4bfd2013db3ce9c719dfcd013"}}