{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EU7FG3MXXBQFELMWSXTPX4NDHU","short_pith_number":"pith:EU7FG3MX","canonical_record":{"source":{"id":"2509.09957","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T04:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"1c4e2cbb574aed93855844acb3c7f7626b92a24ccaabf05ba607784709db7f3c","abstract_canon_sha256":"3d33c28786c1c0ae6e87b72cababdddb3e8dc73d83fdab8741e31e540d8db1f2"},"schema_version":"1.0"},"canonical_sha256":"253e536d97b860522d9695e6fbf1a33d256cb6f962cee9f66e6b2d1b968d4c29","source":{"kind":"arxiv","id":"2509.09957","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.09957","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2509.09957v3","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.09957","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"EU7FG3MXXBQF","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"EU7FG3MXXBQFELMW","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"EU7FG3MX","created_at":"2026-05-21T01:05:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EU7FG3MXXBQFELMWSXTPX4NDHU","target":"record","payload":{"canonical_record":{"source":{"id":"2509.09957","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T04:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"1c4e2cbb574aed93855844acb3c7f7626b92a24ccaabf05ba607784709db7f3c","abstract_canon_sha256":"3d33c28786c1c0ae6e87b72cababdddb3e8dc73d83fdab8741e31e540d8db1f2"},"schema_version":"1.0"},"canonical_sha256":"253e536d97b860522d9695e6fbf1a33d256cb6f962cee9f66e6b2d1b968d4c29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:08.786782Z","signature_b64":"1sm3HDrmFCMr1RjVzkfEZ5EC7zn2uSRlyeNc2wibyUOot8csudcDtVcKlJFQzZSOobKx11z3YcCLcCObMJm9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"253e536d97b860522d9695e6fbf1a33d256cb6f962cee9f66e6b2d1b968d4c29","last_reissued_at":"2026-05-21T01:05:08.785889Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:08.785889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.09957","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":"2026-05-21T01:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sZ9+rjYqDAHomHM6CTrVOPeuqnapz/uxGvI5cb3ygNvgEt/PRh5A0bUMzJRDHQWX1GMBOjIg9vqZquS5h+RODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:02:25.853754Z"},"content_sha256":"59737375241a18993a443f377b3d5d341aaa0ad9e949b51dee18aef57b10a378","schema_version":"1.0","event_id":"sha256:59737375241a18993a443f377b3d5d341aaa0ad9e949b51dee18aef57b10a378"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EU7FG3MXXBQFELMWSXTPX4NDHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spare Strategy Analysis and Design for Mega Satellite Constellations Using Markov Chain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Koki Ho, Seungyeop Han, Shoji Yoshikawa, Takumi Noro, Takumi Suda, Zachary Grieser","submitted_at":"2025-09-12T04:14:52Z","abstract_excerpt":"This paper presents a Markov-chain-based method for the early-phase analysis and design of spare-management architectures for large-scale satellite constellations. To assess the long-run viability of such concepts of operations, satellite failure and replenishment processes are modeled as Markov chains and analyzed through their stationary solution. We reinvestigate an indirect spare strategy, modeled as a multi-echelon periodic-review reorder-point/order-quantity policy, in which spares are first delivered to parking orbits and then transferred to constellation planes. The stock levels in con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09957","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/2509.09957/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":"2026-05-21T01:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+YgIpE0mTHWsV8t/saa9tap5gCm+K0ObWeiQRVXZx82ChpY4TlRkmfCOiRuZDiodTThNaU2nh+yP+GtGZXMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:02:25.854495Z"},"content_sha256":"9460070accab12ff8858d5972e8ceb55415d44006384c3ea88b1fcc057d2b58a","schema_version":"1.0","event_id":"sha256:9460070accab12ff8858d5972e8ceb55415d44006384c3ea88b1fcc057d2b58a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EU7FG3MXXBQFELMWSXTPX4NDHU/bundle.json","state_url":"https://pith.science/pith/EU7FG3MXXBQFELMWSXTPX4NDHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EU7FG3MXXBQFELMWSXTPX4NDHU/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":"2026-05-23T03:02:25Z","links":{"resolver":"https://pith.science/pith/EU7FG3MXXBQFELMWSXTPX4NDHU","bundle":"https://pith.science/pith/EU7FG3MXXBQFELMWSXTPX4NDHU/bundle.json","state":"https://pith.science/pith/EU7FG3MXXBQFELMWSXTPX4NDHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EU7FG3MXXBQFELMWSXTPX4NDHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EU7FG3MXXBQFELMWSXTPX4NDHU","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":"3d33c28786c1c0ae6e87b72cababdddb3e8dc73d83fdab8741e31e540d8db1f2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T04:14:52Z","title_canon_sha256":"1c4e2cbb574aed93855844acb3c7f7626b92a24ccaabf05ba607784709db7f3c"},"schema_version":"1.0","source":{"id":"2509.09957","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.09957","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2509.09957v3","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.09957","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"EU7FG3MXXBQF","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"EU7FG3MXXBQFELMW","created_at":"2026-05-21T01:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"EU7FG3MX","created_at":"2026-05-21T01:05:08Z"}],"graph_snapshots":[{"event_id":"sha256:9460070accab12ff8858d5972e8ceb55415d44006384c3ea88b1fcc057d2b58a","target":"graph","created_at":"2026-05-21T01:05:08Z","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/2509.09957/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents a Markov-chain-based method for the early-phase analysis and design of spare-management architectures for large-scale satellite constellations. To assess the long-run viability of such concepts of operations, satellite failure and replenishment processes are modeled as Markov chains and analyzed through their stationary solution. We reinvestigate an indirect spare strategy, modeled as a multi-echelon periodic-review reorder-point/order-quantity policy, in which spares are first delivered to parking orbits and then transferred to constellation planes. The stock levels in con","authors_text":"Koki Ho, Seungyeop Han, Shoji Yoshikawa, Takumi Noro, Takumi Suda, Zachary Grieser","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T04:14:52Z","title":"Spare Strategy Analysis and Design for Mega Satellite Constellations Using Markov Chain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09957","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":"sha256:59737375241a18993a443f377b3d5d341aaa0ad9e949b51dee18aef57b10a378","target":"record","created_at":"2026-05-21T01:05:08Z","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":"3d33c28786c1c0ae6e87b72cababdddb3e8dc73d83fdab8741e31e540d8db1f2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T04:14:52Z","title_canon_sha256":"1c4e2cbb574aed93855844acb3c7f7626b92a24ccaabf05ba607784709db7f3c"},"schema_version":"1.0","source":{"id":"2509.09957","kind":"arxiv","version":3}},"canonical_sha256":"253e536d97b860522d9695e6fbf1a33d256cb6f962cee9f66e6b2d1b968d4c29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"253e536d97b860522d9695e6fbf1a33d256cb6f962cee9f66e6b2d1b968d4c29","first_computed_at":"2026-05-21T01:05:08.785889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:08.785889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1sm3HDrmFCMr1RjVzkfEZ5EC7zn2uSRlyeNc2wibyUOot8csudcDtVcKlJFQzZSOobKx11z3YcCLcCObMJm9BA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:08.786782Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.09957","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59737375241a18993a443f377b3d5d341aaa0ad9e949b51dee18aef57b10a378","sha256:9460070accab12ff8858d5972e8ceb55415d44006384c3ea88b1fcc057d2b58a"],"state_sha256":"8b51488059ca2727916f9f0b944a5b41249d5c7b5748fe1ebad57c4e19765e3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCJ7NyN+hNMP4wnGSzPiyRQ1Jdpq1a73A48bd9bngXMN1+3LfxlxQSyY0BcWrlVpHg0h6qEeX/f89ag9Xf3zCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T03:02:25.858343Z","bundle_sha256":"1a7d3cb599317abd9f94d301946080917fb9a3c660c2f3ff7947fa3d22918c48"}}