{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:D2IA46PTTAQXBBEOQZIYIDDN4H","short_pith_number":"pith:D2IA46PT","canonical_record":{"source":{"id":"cond-mat/9708147","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"1997-08-20T02:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"4d7c9e5edd9206050144258ef83f8d051b8cab5e416981376a10ff054e285c94","abstract_canon_sha256":"e3bf01bb38e316b71f65d77548399119320427b57e5f7317d2af60a46b9bbbae"},"schema_version":"1.0"},"canonical_sha256":"1e900e79f3982170848e8651840c6de1e2e6a75e498055b14822018ce90fe087","source":{"kind":"arxiv","id":"cond-mat/9708147","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9708147","created_at":"2026-05-18T01:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9708147v1","created_at":"2026-05-18T01:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9708147","created_at":"2026-05-18T01:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"D2IA46PTTAQX","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"D2IA46PTTAQXBBEO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"D2IA46PT","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:D2IA46PTTAQXBBEOQZIYIDDN4H","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9708147","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"1997-08-20T02:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"4d7c9e5edd9206050144258ef83f8d051b8cab5e416981376a10ff054e285c94","abstract_canon_sha256":"e3bf01bb38e316b71f65d77548399119320427b57e5f7317d2af60a46b9bbbae"},"schema_version":"1.0"},"canonical_sha256":"1e900e79f3982170848e8651840c6de1e2e6a75e498055b14822018ce90fe087","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:07.939480Z","signature_b64":"M6i8/Sdeuuw5O5zKQKSAKRIEQ5Mxp/mb9PJynrGQ7ShU405H7QRv+jG0pUUgD1u5lNIbP+ZqNxpkfDjzE6ixBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e900e79f3982170848e8651840c6de1e2e6a75e498055b14822018ce90fe087","last_reissued_at":"2026-05-18T01:07:07.938923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:07.938923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9708147","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":"2026-05-18T01:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"701c6kHa59ZmaD52ZrC+q/T/QU/b0BFqkOXJCDP+9AGuCm2h6p8xOfHPRZmNxUn3VQ0rXGApEG5pafGqtYSmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:03:27.318501Z"},"content_sha256":"98bd292a993ba030d6a774d23349237d2c81142e8c282ba34d6f5c8b6e624799","schema_version":"1.0","event_id":"sha256:98bd292a993ba030d6a774d23349237d2c81142e8c282ba34d6f5c8b6e624799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:D2IA46PTTAQXBBEOQZIYIDDN4H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical mechanics of the multi-constraint continuous knapsack problem","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Jun-ichi Inoue (Tokyo Institute of Technology, RIKEN)","submitted_at":"1997-08-20T02:22:50Z","abstract_excerpt":"We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large problem size, we analyse the space of solution and its volume, and estimate the optimal number of items to go into the knapsack as a function of the number of constraints. We study the stability of the replica symmetric (RS) solution and find that the RS calculation cannot estimate the optimal number of items in knapsack correctly if many constraints are requi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9708147","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":""},"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":"2026-05-18T01:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cgsGR+xkgmQDEldmx95B7JKDfz2yIFnmLDeZ/ZpuUf62T5ApJjyAKm9pwoMzLY0de6mmZ8sfTJIa4xLq73kuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:03:27.319272Z"},"content_sha256":"7af46c46321f84bd546c9f76f21756e9c874b048157c31ec9329ac302a1f3376","schema_version":"1.0","event_id":"sha256:7af46c46321f84bd546c9f76f21756e9c874b048157c31ec9329ac302a1f3376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2IA46PTTAQXBBEOQZIYIDDN4H/bundle.json","state_url":"https://pith.science/pith/D2IA46PTTAQXBBEOQZIYIDDN4H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2IA46PTTAQXBBEOQZIYIDDN4H/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":"2026-05-31T15:03:27Z","links":{"resolver":"https://pith.science/pith/D2IA46PTTAQXBBEOQZIYIDDN4H","bundle":"https://pith.science/pith/D2IA46PTTAQXBBEOQZIYIDDN4H/bundle.json","state":"https://pith.science/pith/D2IA46PTTAQXBBEOQZIYIDDN4H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2IA46PTTAQXBBEOQZIYIDDN4H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:D2IA46PTTAQXBBEOQZIYIDDN4H","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":"e3bf01bb38e316b71f65d77548399119320427b57e5f7317d2af60a46b9bbbae","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"1997-08-20T02:22:50Z","title_canon_sha256":"4d7c9e5edd9206050144258ef83f8d051b8cab5e416981376a10ff054e285c94"},"schema_version":"1.0","source":{"id":"cond-mat/9708147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9708147","created_at":"2026-05-18T01:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9708147v1","created_at":"2026-05-18T01:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9708147","created_at":"2026-05-18T01:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"D2IA46PTTAQX","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"D2IA46PTTAQXBBEO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"D2IA46PT","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:7af46c46321f84bd546c9f76f21756e9c874b048157c31ec9329ac302a1f3376","target":"graph","created_at":"2026-05-18T01:07:07Z","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"},"paper":{"abstract_excerpt":"We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large problem size, we analyse the space of solution and its volume, and estimate the optimal number of items to go into the knapsack as a function of the number of constraints. We study the stability of the replica symmetric (RS) solution and find that the RS calculation cannot estimate the optimal number of items in knapsack correctly if many constraints are requi","authors_text":"Jun-ichi Inoue (Tokyo Institute of Technology, RIKEN)","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"1997-08-20T02:22:50Z","title":"Statistical mechanics of the multi-constraint continuous knapsack problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9708147","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":"sha256:98bd292a993ba030d6a774d23349237d2c81142e8c282ba34d6f5c8b6e624799","target":"record","created_at":"2026-05-18T01:07:07Z","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":"e3bf01bb38e316b71f65d77548399119320427b57e5f7317d2af60a46b9bbbae","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"1997-08-20T02:22:50Z","title_canon_sha256":"4d7c9e5edd9206050144258ef83f8d051b8cab5e416981376a10ff054e285c94"},"schema_version":"1.0","source":{"id":"cond-mat/9708147","kind":"arxiv","version":1}},"canonical_sha256":"1e900e79f3982170848e8651840c6de1e2e6a75e498055b14822018ce90fe087","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e900e79f3982170848e8651840c6de1e2e6a75e498055b14822018ce90fe087","first_computed_at":"2026-05-18T01:07:07.938923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:07.938923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M6i8/Sdeuuw5O5zKQKSAKRIEQ5Mxp/mb9PJynrGQ7ShU405H7QRv+jG0pUUgD1u5lNIbP+ZqNxpkfDjzE6ixBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:07.939480Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9708147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98bd292a993ba030d6a774d23349237d2c81142e8c282ba34d6f5c8b6e624799","sha256:7af46c46321f84bd546c9f76f21756e9c874b048157c31ec9329ac302a1f3376"],"state_sha256":"b489a81b2d51f92b2e1e3fb33ebc90094a6015b77f403d76812ada32f4a8b8e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VSg6pUMyuxzN9HM2t4uNIxGoIViVs0uifkOGrpMm9qNtgOuR/DQE4ZBVMuKssHebmsE7wj/z0OurIW2QpnrZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:03:27.323822Z","bundle_sha256":"65dd94fa3bd94ed0f8a67c8c7ea2901843611a62c33d2f96b71aeed68a2e30f3"}}