{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E25IOBR75QOTC3ENR4KBU75C5F","short_pith_number":"pith:E25IOBR7","canonical_record":{"source":{"id":"2607.24120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-27T07:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"fb73b1db1cc28f550b9c138e52c1fb18363535a097f460a79ac62f914d3b036c","abstract_canon_sha256":"eb5582bfd3054ee6bf6a1e3c92d7e30c0ff83d32a8cb7d8e565337400fa0821a"},"schema_version":"1.0"},"canonical_sha256":"26ba87063fec1d316c8d8f141a7fa2e962d9e3fb479ee0a42e68687b3ba4b134","source":{"kind":"arxiv","id":"2607.24120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24120","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24120v1","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24120","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"E25IOBR75QOT","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"pith_short_16","alias_value":"E25IOBR75QOTC3EN","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"pith_short_8","alias_value":"E25IOBR7","created_at":"2026-07-28T01:23:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E25IOBR75QOTC3ENR4KBU75C5F","target":"record","payload":{"canonical_record":{"source":{"id":"2607.24120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-27T07:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"fb73b1db1cc28f550b9c138e52c1fb18363535a097f460a79ac62f914d3b036c","abstract_canon_sha256":"eb5582bfd3054ee6bf6a1e3c92d7e30c0ff83d32a8cb7d8e565337400fa0821a"},"schema_version":"1.0"},"canonical_sha256":"26ba87063fec1d316c8d8f141a7fa2e962d9e3fb479ee0a42e68687b3ba4b134","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:23:46.156043Z","signature_b64":"pMGOWUm1zwN4ZcYJRwumpIDg7sxXZWWRXHu2Xsr1m9T2txoXcn10G2s514uI1ime9OYq0ABBi0P4e3epr0McBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26ba87063fec1d316c8d8f141a7fa2e962d9e3fb479ee0a42e68687b3ba4b134","last_reissued_at":"2026-07-28T01:23:46.155209Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:23:46.155209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.24120","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":"2026-07-28T01:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DEBuMtI/FgXjW0htuVIH/F6YzCQr4Jk+d9qrZt57nE59nnIysV3N1Ja4ZPjxSwFmAoG0WB1+RvBlS+Go6/UUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:41:36.583109Z"},"content_sha256":"bbd7db50139df979b6a6b4b61f193082fe73bd03ee6ccf88454164aff0784a14","schema_version":"1.0","event_id":"sha256:bbd7db50139df979b6a6b4b61f193082fe73bd03ee6ccf88454164aff0784a14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E25IOBR75QOTC3ENR4KBU75C5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the hardness of deterministic second-order optimization of functions with Lipschitz gradients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Anthony Man-Cho So, Jiewen Guan","submitted_at":"2026-07-27T07:59:39Z","abstract_excerpt":"We show that no deterministic zero-respecting algorithm (resp., (general) deterministic algorithm) can compute Goldstein approximate second-order stationary points of functions with Lipschitz continuous gradients within a finite number of (resp., no more than $n-3$ with $n$ being the input dimension) second-order oracle calls. This, among other consequences, shows that deterministic second-order weakly convex optimization is intractable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24120","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/2607.24120/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":"2026-07-28T01:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZzrh6ddZXuMMKiu79PR/Vl51j8kc8gDCw1gX1y69NeE3gM5EVTXMF7jXC1VQmVD72NMOkulKpX1tmuKwvQ+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:41:36.583588Z"},"content_sha256":"2065f9a35d9ea2f3b00bca35cf73e4a7aa148dc80d4db30b58465fe7725baf01","schema_version":"1.0","event_id":"sha256:2065f9a35d9ea2f3b00bca35cf73e4a7aa148dc80d4db30b58465fe7725baf01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E25IOBR75QOTC3ENR4KBU75C5F/bundle.json","state_url":"https://pith.science/pith/E25IOBR75QOTC3ENR4KBU75C5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E25IOBR75QOTC3ENR4KBU75C5F/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":"2026-08-09T00:41:36Z","links":{"resolver":"https://pith.science/pith/E25IOBR75QOTC3ENR4KBU75C5F","bundle":"https://pith.science/pith/E25IOBR75QOTC3ENR4KBU75C5F/bundle.json","state":"https://pith.science/pith/E25IOBR75QOTC3ENR4KBU75C5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E25IOBR75QOTC3ENR4KBU75C5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E25IOBR75QOTC3ENR4KBU75C5F","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":"eb5582bfd3054ee6bf6a1e3c92d7e30c0ff83d32a8cb7d8e565337400fa0821a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-27T07:59:39Z","title_canon_sha256":"fb73b1db1cc28f550b9c138e52c1fb18363535a097f460a79ac62f914d3b036c"},"schema_version":"1.0","source":{"id":"2607.24120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24120","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24120v1","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24120","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"E25IOBR75QOT","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"pith_short_16","alias_value":"E25IOBR75QOTC3EN","created_at":"2026-07-28T01:23:46Z"},{"alias_kind":"pith_short_8","alias_value":"E25IOBR7","created_at":"2026-07-28T01:23:46Z"}],"graph_snapshots":[{"event_id":"sha256:2065f9a35d9ea2f3b00bca35cf73e4a7aa148dc80d4db30b58465fe7725baf01","target":"graph","created_at":"2026-07-28T01:23:46Z","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/2607.24120/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that no deterministic zero-respecting algorithm (resp., (general) deterministic algorithm) can compute Goldstein approximate second-order stationary points of functions with Lipschitz continuous gradients within a finite number of (resp., no more than $n-3$ with $n$ being the input dimension) second-order oracle calls. This, among other consequences, shows that deterministic second-order weakly convex optimization is intractable.","authors_text":"Anthony Man-Cho So, Jiewen Guan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-27T07:59:39Z","title":"On the hardness of deterministic second-order optimization of functions with Lipschitz gradients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24120","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:bbd7db50139df979b6a6b4b61f193082fe73bd03ee6ccf88454164aff0784a14","target":"record","created_at":"2026-07-28T01:23:46Z","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":"eb5582bfd3054ee6bf6a1e3c92d7e30c0ff83d32a8cb7d8e565337400fa0821a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-27T07:59:39Z","title_canon_sha256":"fb73b1db1cc28f550b9c138e52c1fb18363535a097f460a79ac62f914d3b036c"},"schema_version":"1.0","source":{"id":"2607.24120","kind":"arxiv","version":1}},"canonical_sha256":"26ba87063fec1d316c8d8f141a7fa2e962d9e3fb479ee0a42e68687b3ba4b134","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26ba87063fec1d316c8d8f141a7fa2e962d9e3fb479ee0a42e68687b3ba4b134","first_computed_at":"2026-07-28T01:23:46.155209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:23:46.155209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pMGOWUm1zwN4ZcYJRwumpIDg7sxXZWWRXHu2Xsr1m9T2txoXcn10G2s514uI1ime9OYq0ABBi0P4e3epr0McBQ==","signature_status":"signed_v1","signed_at":"2026-07-28T01:23:46.156043Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.24120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbd7db50139df979b6a6b4b61f193082fe73bd03ee6ccf88454164aff0784a14","sha256:2065f9a35d9ea2f3b00bca35cf73e4a7aa148dc80d4db30b58465fe7725baf01"],"state_sha256":"389b350a54fb964196fb539da6e867ec2ee8a9e1216b93e094b9d8787c1dd55c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jfg2nxCD590CX0c/0HG8f7dmgZqYWUXfHo3wEqOSh5YnbCNuHMNbK82dXTehiwEm+VlrT7snsrAXnVGhKZmWAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:41:36.587089Z","bundle_sha256":"4e4135cfbd403956770aef74aefaacaa2666ee4a004d72eb42f704ba521a432f"}}