{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UCQ7PQNTSBNAX3YIMNNRRPXLZN","short_pith_number":"pith:UCQ7PQNT","canonical_record":{"source":{"id":"1108.4972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-08-25T00:44:13Z","cross_cats_sorted":[],"title_canon_sha256":"fd06ce829a3c875a7347411aebd0030654cdf37eb4163b6024aa189f11bd284c","abstract_canon_sha256":"34838e28747428759f1dd75ef0ae3219468183c57a4e79123ee96b8d27bbd456"},"schema_version":"1.0"},"canonical_sha256":"a0a1f7c1b3905a0bef08635b18beebcb55da6a1e5529b55374f8346f998c2c54","source":{"kind":"arxiv","id":"1108.4972","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4972","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4972v1","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4972","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"pith_short_12","alias_value":"UCQ7PQNTSBNA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UCQ7PQNTSBNAX3YI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UCQ7PQNT","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UCQ7PQNTSBNAX3YIMNNRRPXLZN","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-08-25T00:44:13Z","cross_cats_sorted":[],"title_canon_sha256":"fd06ce829a3c875a7347411aebd0030654cdf37eb4163b6024aa189f11bd284c","abstract_canon_sha256":"34838e28747428759f1dd75ef0ae3219468183c57a4e79123ee96b8d27bbd456"},"schema_version":"1.0"},"canonical_sha256":"a0a1f7c1b3905a0bef08635b18beebcb55da6a1e5529b55374f8346f998c2c54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:37.088235Z","signature_b64":"SjDoerrEfuB6c+X7wfYTc1ifpqikIZmQRdKo02QNq6aZutx8TAK1w+hli5JXe0mzu+EoTA/F0tfvz0KtPQpfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0a1f7c1b3905a0bef08635b18beebcb55da6a1e5529b55374f8346f998c2c54","last_reissued_at":"2026-05-18T02:21:37.087799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:37.087799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4972","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":"2026-05-18T02:21:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N9HX6xVfNZ8zQaybrldbVrmVz8qtgYVHPVm8Nr12jkP7857AVYF1P2m6YkWsRj+l6Rs7XzjIVbaHYYS5zJvhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:18:34.553996Z"},"content_sha256":"8323c3ce8dba5d618a24d3a4c72d0321e9d10ef603b8aab718695508e4b00f87","schema_version":"1.0","event_id":"sha256:8323c3ce8dba5d618a24d3a4c72d0321e9d10ef603b8aab718695508e4b00f87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UCQ7PQNTSBNAX3YIMNNRRPXLZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms for the Problems of Length-Constrained Heaviest Segments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Asish Mukhopadhyay, Md. Shafiul Alam","submitted_at":"2011-08-25T00:44:13Z","abstract_excerpt":"We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a sequence of n real numbers and two real parameters L and U (L <= U), the maximum sum segment problem is to find a consecutive subsequence, called a segment, of length at least L and at most U such that the sum of the numbers in the subsequence is maximum. The maximum density segment problem is to find a segment of length at least L and at most U such that the den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4972","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":"2026-05-18T02:21:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reoFmhWTXXH6D2sKE7/zuFsdiZ5eOqc4ZbGIxHD/xo00nKCtz8wzu05rHb+5ZCDLUZksxgKpGjdNzbYkA38lCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:18:34.554346Z"},"content_sha256":"85934a048785fcb21a60eab005b6f25d726e808e67825cd701718684953ea9ff","schema_version":"1.0","event_id":"sha256:85934a048785fcb21a60eab005b6f25d726e808e67825cd701718684953ea9ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UCQ7PQNTSBNAX3YIMNNRRPXLZN/bundle.json","state_url":"https://pith.science/pith/UCQ7PQNTSBNAX3YIMNNRRPXLZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UCQ7PQNTSBNAX3YIMNNRRPXLZN/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":"2026-06-30T15:18:34Z","links":{"resolver":"https://pith.science/pith/UCQ7PQNTSBNAX3YIMNNRRPXLZN","bundle":"https://pith.science/pith/UCQ7PQNTSBNAX3YIMNNRRPXLZN/bundle.json","state":"https://pith.science/pith/UCQ7PQNTSBNAX3YIMNNRRPXLZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UCQ7PQNTSBNAX3YIMNNRRPXLZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UCQ7PQNTSBNAX3YIMNNRRPXLZN","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":"34838e28747428759f1dd75ef0ae3219468183c57a4e79123ee96b8d27bbd456","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-08-25T00:44:13Z","title_canon_sha256":"fd06ce829a3c875a7347411aebd0030654cdf37eb4163b6024aa189f11bd284c"},"schema_version":"1.0","source":{"id":"1108.4972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4972","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4972v1","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4972","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"pith_short_12","alias_value":"UCQ7PQNTSBNA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UCQ7PQNTSBNAX3YI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UCQ7PQNT","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:85934a048785fcb21a60eab005b6f25d726e808e67825cd701718684953ea9ff","target":"graph","created_at":"2026-05-18T02:21:37Z","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 present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a sequence of n real numbers and two real parameters L and U (L <= U), the maximum sum segment problem is to find a consecutive subsequence, called a segment, of length at least L and at most U such that the sum of the numbers in the subsequence is maximum. The maximum density segment problem is to find a segment of length at least L and at most U such that the den","authors_text":"Asish Mukhopadhyay, Md. Shafiul Alam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-08-25T00:44:13Z","title":"Algorithms for the Problems of Length-Constrained Heaviest Segments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4972","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":"sha256:8323c3ce8dba5d618a24d3a4c72d0321e9d10ef603b8aab718695508e4b00f87","target":"record","created_at":"2026-05-18T02:21:37Z","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":"34838e28747428759f1dd75ef0ae3219468183c57a4e79123ee96b8d27bbd456","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-08-25T00:44:13Z","title_canon_sha256":"fd06ce829a3c875a7347411aebd0030654cdf37eb4163b6024aa189f11bd284c"},"schema_version":"1.0","source":{"id":"1108.4972","kind":"arxiv","version":1}},"canonical_sha256":"a0a1f7c1b3905a0bef08635b18beebcb55da6a1e5529b55374f8346f998c2c54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0a1f7c1b3905a0bef08635b18beebcb55da6a1e5529b55374f8346f998c2c54","first_computed_at":"2026-05-18T02:21:37.087799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:37.087799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SjDoerrEfuB6c+X7wfYTc1ifpqikIZmQRdKo02QNq6aZutx8TAK1w+hli5JXe0mzu+EoTA/F0tfvz0KtPQpfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:37.088235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8323c3ce8dba5d618a24d3a4c72d0321e9d10ef603b8aab718695508e4b00f87","sha256:85934a048785fcb21a60eab005b6f25d726e808e67825cd701718684953ea9ff"],"state_sha256":"5bf3b702d823a4a3ffab12681e8d275fbcb550836e12fc105432d9f0d885ff59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCtsw55o7NrBry2FldhFJ6uWF2tuSoTMwjwrMwzMIO2oCBYM7JJ39Eu9kZnKCGcd+HlBOddFNN6POhIuZSHnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T15:18:34.556201Z","bundle_sha256":"ee6fd7f2232f982069f0af82f549a531b2d4d25bfafb8e96a4537750fd3e9568"}}