{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:2EGPWF6VQDDEDEGMSVKHUHHNXH","short_pith_number":"pith:2EGPWF6V","canonical_record":{"source":{"id":"2307.08986","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-18T05:56:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"60f5a3122efd4c35f2b0e8f979fbae3579e99d06a0b055ee391b926f5c060109","abstract_canon_sha256":"da4d67575fbc896c8e0cb000049a3e4558842d6889a84f6c73bc4e7f12728e11"},"schema_version":"1.0"},"canonical_sha256":"d10cfb17d580c64190cc95547a1cedb9f1b20800f18d2f55566484ffbb753784","source":{"kind":"arxiv","id":"2307.08986","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.08986","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"2307.08986v3","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.08986","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"2EGPWF6VQDDE","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"pith_short_16","alias_value":"2EGPWF6VQDDEDEGM","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"pith_short_8","alias_value":"2EGPWF6V","created_at":"2026-07-05T08:04:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:2EGPWF6VQDDEDEGMSVKHUHHNXH","target":"record","payload":{"canonical_record":{"source":{"id":"2307.08986","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-18T05:56:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"60f5a3122efd4c35f2b0e8f979fbae3579e99d06a0b055ee391b926f5c060109","abstract_canon_sha256":"da4d67575fbc896c8e0cb000049a3e4558842d6889a84f6c73bc4e7f12728e11"},"schema_version":"1.0"},"canonical_sha256":"d10cfb17d580c64190cc95547a1cedb9f1b20800f18d2f55566484ffbb753784","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:13.437810Z","signature_b64":"kK7Bbidai8zhlzgiw8x8IPl8LY7OkQRUqhgLkuYeQQ8VKAeq8tkEn0XJUy1tzj6TEpAK1V1oC2WrJzkAYjW2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d10cfb17d580c64190cc95547a1cedb9f1b20800f18d2f55566484ffbb753784","last_reissued_at":"2026-07-05T08:04:13.437352Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:13.437352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.08986","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":"2026-07-05T08:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aMO+by2VpZrJeZ7YM9fZHdNXhFKYw+UfM6t7C8RCxTK/4wUpnkg6HQShpvME/RzF+COeuDatvGfOziURYTtuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:25:10.253151Z"},"content_sha256":"ebbd5c3295873226bac8585c39e97855db1f579618263d96861e8225ea9e3252","schema_version":"1.0","event_id":"sha256:ebbd5c3295873226bac8585c39e97855db1f579618263d96861e8225ea9e3252"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:2EGPWF6VQDDEDEGMSVKHUHHNXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modified memoryless spectral-scaling Broyden family on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hideaki Iiduka, Hiroyuki Sakai","submitted_at":"2023-07-18T05:56:57Z","abstract_excerpt":"This paper presents modified memoryless quasi-Newton methods based on the spectral-scaling Broyden family on Riemannian manifolds. The method involves adding one parameter to the search direction of the memoryless self-scaling Broyden family on the manifold. Moreover, it uses a general map instead of vector transport. This idea has already been proposed within a general framework of Riemannian conjugate gradient methods where one can use vector transport, scaled vector transport, or an inverse retraction. We show that the search direction satisfies the sufficient descent condition under some a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08986","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/2307.08986/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":"2026-07-05T08:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"96CCxf32bf5RgsXwyRVyoy6/xdRL7BPCd1bDZBI5JWJLMpxmBU0SZqpCcqFEjCuEEfs6150cxpIRdkG+IzRKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:25:10.253704Z"},"content_sha256":"c5c551eb5d17ab1bfed42505747281b6385aea05120a5e8ec708d36ad4ad3e80","schema_version":"1.0","event_id":"sha256:c5c551eb5d17ab1bfed42505747281b6385aea05120a5e8ec708d36ad4ad3e80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2EGPWF6VQDDEDEGMSVKHUHHNXH/bundle.json","state_url":"https://pith.science/pith/2EGPWF6VQDDEDEGMSVKHUHHNXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2EGPWF6VQDDEDEGMSVKHUHHNXH/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":"2026-08-18T14:25:10Z","links":{"resolver":"https://pith.science/pith/2EGPWF6VQDDEDEGMSVKHUHHNXH","bundle":"https://pith.science/pith/2EGPWF6VQDDEDEGMSVKHUHHNXH/bundle.json","state":"https://pith.science/pith/2EGPWF6VQDDEDEGMSVKHUHHNXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2EGPWF6VQDDEDEGMSVKHUHHNXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2EGPWF6VQDDEDEGMSVKHUHHNXH","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":"da4d67575fbc896c8e0cb000049a3e4558842d6889a84f6c73bc4e7f12728e11","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-18T05:56:57Z","title_canon_sha256":"60f5a3122efd4c35f2b0e8f979fbae3579e99d06a0b055ee391b926f5c060109"},"schema_version":"1.0","source":{"id":"2307.08986","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.08986","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"2307.08986v3","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.08986","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"2EGPWF6VQDDE","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"pith_short_16","alias_value":"2EGPWF6VQDDEDEGM","created_at":"2026-07-05T08:04:13Z"},{"alias_kind":"pith_short_8","alias_value":"2EGPWF6V","created_at":"2026-07-05T08:04:13Z"}],"graph_snapshots":[{"event_id":"sha256:c5c551eb5d17ab1bfed42505747281b6385aea05120a5e8ec708d36ad4ad3e80","target":"graph","created_at":"2026-07-05T08:04:13Z","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/2307.08986/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents modified memoryless quasi-Newton methods based on the spectral-scaling Broyden family on Riemannian manifolds. The method involves adding one parameter to the search direction of the memoryless self-scaling Broyden family on the manifold. Moreover, it uses a general map instead of vector transport. This idea has already been proposed within a general framework of Riemannian conjugate gradient methods where one can use vector transport, scaled vector transport, or an inverse retraction. We show that the search direction satisfies the sufficient descent condition under some a","authors_text":"Hideaki Iiduka, Hiroyuki Sakai","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-18T05:56:57Z","title":"Modified memoryless spectral-scaling Broyden family on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08986","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:ebbd5c3295873226bac8585c39e97855db1f579618263d96861e8225ea9e3252","target":"record","created_at":"2026-07-05T08:04:13Z","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":"da4d67575fbc896c8e0cb000049a3e4558842d6889a84f6c73bc4e7f12728e11","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-18T05:56:57Z","title_canon_sha256":"60f5a3122efd4c35f2b0e8f979fbae3579e99d06a0b055ee391b926f5c060109"},"schema_version":"1.0","source":{"id":"2307.08986","kind":"arxiv","version":3}},"canonical_sha256":"d10cfb17d580c64190cc95547a1cedb9f1b20800f18d2f55566484ffbb753784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d10cfb17d580c64190cc95547a1cedb9f1b20800f18d2f55566484ffbb753784","first_computed_at":"2026-07-05T08:04:13.437352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:04:13.437352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kK7Bbidai8zhlzgiw8x8IPl8LY7OkQRUqhgLkuYeQQ8VKAeq8tkEn0XJUy1tzj6TEpAK1V1oC2WrJzkAYjW2Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:04:13.437810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.08986","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebbd5c3295873226bac8585c39e97855db1f579618263d96861e8225ea9e3252","sha256:c5c551eb5d17ab1bfed42505747281b6385aea05120a5e8ec708d36ad4ad3e80"],"state_sha256":"d4ac6ec738498e5a5663947e3de3821f9179c70fe1fe8730f662f91f6e4b637a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fq/ZsNZEGYlR8L403fiYA3hbDwo/MpRYSovHT6QCjopSqiDLamFl5i4es+RLy3ewjPIaQgQp1zSXviOaExQrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T14:25:10.260379Z","bundle_sha256":"c3cf8038fd9c2fba387d599750adcccd9bb0183152de043e91d018e50a67eca8"}}