{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2AFWNMIEUH3PIXMMC5Y7ZYUIKJ","short_pith_number":"pith:2AFWNMIE","canonical_record":{"source":{"id":"1404.1087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T20:20:05Z","cross_cats_sorted":[],"title_canon_sha256":"6a7d6585ae24e45e19cd8fa135a8a4373c7a9f691aef515a64fcf83fe3d519b3","abstract_canon_sha256":"a91a7125a6912ea1805b9ef16b79c0bbc6b6e8e2c04638d3c82733ba9eb60c34"},"schema_version":"1.0"},"canonical_sha256":"d00b66b104a1f6f45d8c1771fce2885242335cc50d9e5ff425a60ced7fa805c5","source":{"kind":"arxiv","id":"1404.1087","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1087","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1087v1","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1087","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"2AFWNMIEUH3P","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2AFWNMIEUH3PIXMM","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2AFWNMIE","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2AFWNMIEUH3PIXMMC5Y7ZYUIKJ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T20:20:05Z","cross_cats_sorted":[],"title_canon_sha256":"6a7d6585ae24e45e19cd8fa135a8a4373c7a9f691aef515a64fcf83fe3d519b3","abstract_canon_sha256":"a91a7125a6912ea1805b9ef16b79c0bbc6b6e8e2c04638d3c82733ba9eb60c34"},"schema_version":"1.0"},"canonical_sha256":"d00b66b104a1f6f45d8c1771fce2885242335cc50d9e5ff425a60ced7fa805c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:54.235453Z","signature_b64":"vqDYPhDmD+seVpckVJJkW0oIHDUInGxje7wEpInvOy4O2UXZx+JfRES+wIHuSDax+vHcl2oKABCaQ2OgifamBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d00b66b104a1f6f45d8c1771fce2885242335cc50d9e5ff425a60ced7fa805c5","last_reissued_at":"2026-05-18T02:54:54.234894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:54.234894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1087","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":"2026-05-18T02:54:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2WvX8yBtuJnOF455NggU76utEY3lSsWh/YyzQCDR/pJyUF76ypD8WCouKJERNjHO3QB8osD7ESzmXhq4jwbNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:03:47.108752Z"},"content_sha256":"ff5d13b77889e3bfe2ac40504ae46c993f835af489c23a49c24baa0ae51f4482","schema_version":"1.0","event_id":"sha256:ff5d13b77889e3bfe2ac40504ae46c993f835af489c23a49c24baa0ae51f4482"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2AFWNMIEUH3PIXMMC5Y7ZYUIKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Windows Scheduling with Reallocation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christopher Thraves, Katia Leal, Martin Farach-Colton, Miguel A. Mosteiro","submitted_at":"2014-04-03T20:20:05Z","abstract_excerpt":"We consider the Windows Scheduling problem. The problem is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels to clients. Each client ci is characterized by an active cycle and a window wi. During the period of time that any given client ci is active, there must be at least one transmission from ci scheduled in any wi consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1087","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":"2026-05-18T02:54:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBVPTAxusqY0eUaUNzXAYSEoxaFKK8p12UVDota9MsbGDpyFoM/nd8qDh4GBV/d+Pygs9cPGk5C6ZRZFH0lSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:03:47.109119Z"},"content_sha256":"e249fce1d33ce12c2deb64be2b3c9d10a21c0d336271650addcb226018f4f5cc","schema_version":"1.0","event_id":"sha256:e249fce1d33ce12c2deb64be2b3c9d10a21c0d336271650addcb226018f4f5cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AFWNMIEUH3PIXMMC5Y7ZYUIKJ/bundle.json","state_url":"https://pith.science/pith/2AFWNMIEUH3PIXMMC5Y7ZYUIKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AFWNMIEUH3PIXMMC5Y7ZYUIKJ/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":"2026-05-30T06:03:47Z","links":{"resolver":"https://pith.science/pith/2AFWNMIEUH3PIXMMC5Y7ZYUIKJ","bundle":"https://pith.science/pith/2AFWNMIEUH3PIXMMC5Y7ZYUIKJ/bundle.json","state":"https://pith.science/pith/2AFWNMIEUH3PIXMMC5Y7ZYUIKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AFWNMIEUH3PIXMMC5Y7ZYUIKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2AFWNMIEUH3PIXMMC5Y7ZYUIKJ","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":"a91a7125a6912ea1805b9ef16b79c0bbc6b6e8e2c04638d3c82733ba9eb60c34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T20:20:05Z","title_canon_sha256":"6a7d6585ae24e45e19cd8fa135a8a4373c7a9f691aef515a64fcf83fe3d519b3"},"schema_version":"1.0","source":{"id":"1404.1087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1087","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1087v1","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1087","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"2AFWNMIEUH3P","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2AFWNMIEUH3PIXMM","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2AFWNMIE","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:e249fce1d33ce12c2deb64be2b3c9d10a21c0d336271650addcb226018f4f5cc","target":"graph","created_at":"2026-05-18T02:54:54Z","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 consider the Windows Scheduling problem. The problem is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels to clients. Each client ci is characterized by an active cycle and a window wi. During the period of time that any given client ci is active, there must be at least one transmission from ci scheduled in any wi consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the","authors_text":"Christopher Thraves, Katia Leal, Martin Farach-Colton, Miguel A. Mosteiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T20:20:05Z","title":"Dynamic Windows Scheduling with Reallocation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1087","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:ff5d13b77889e3bfe2ac40504ae46c993f835af489c23a49c24baa0ae51f4482","target":"record","created_at":"2026-05-18T02:54:54Z","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":"a91a7125a6912ea1805b9ef16b79c0bbc6b6e8e2c04638d3c82733ba9eb60c34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T20:20:05Z","title_canon_sha256":"6a7d6585ae24e45e19cd8fa135a8a4373c7a9f691aef515a64fcf83fe3d519b3"},"schema_version":"1.0","source":{"id":"1404.1087","kind":"arxiv","version":1}},"canonical_sha256":"d00b66b104a1f6f45d8c1771fce2885242335cc50d9e5ff425a60ced7fa805c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d00b66b104a1f6f45d8c1771fce2885242335cc50d9e5ff425a60ced7fa805c5","first_computed_at":"2026-05-18T02:54:54.234894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:54.234894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vqDYPhDmD+seVpckVJJkW0oIHDUInGxje7wEpInvOy4O2UXZx+JfRES+wIHuSDax+vHcl2oKABCaQ2OgifamBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:54.235453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff5d13b77889e3bfe2ac40504ae46c993f835af489c23a49c24baa0ae51f4482","sha256:e249fce1d33ce12c2deb64be2b3c9d10a21c0d336271650addcb226018f4f5cc"],"state_sha256":"0781c060674b56fb2bbbb4ed918f2793804606b373c91105b5b82eab461ff591"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vcW85lcHmd+3VUfV1CV/82c/9qRqDxzSA0duRUseMsPOuXbdthXxw9opdN86AsGjikLSzlczkoKov4ny3aKPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:03:47.111367Z","bundle_sha256":"a63090336c71c6c2ba03e17eb916b56b17325f5fe247df9dc670bf10184cc5da"}}