{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:53EHVBSJ6O5EYMF77WMGZJQHZ3","short_pith_number":"pith:53EHVBSJ","canonical_record":{"source":{"id":"1209.3466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-16T08:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"0be252d6042f2a77796ca9ebc80c95b71c7f8c355e0e2b1e9109b9129c3d1236","abstract_canon_sha256":"051f66badd9635c685612648de1c6b03ac6aa19289617a530cb2616774e51d33"},"schema_version":"1.0"},"canonical_sha256":"eec87a8649f3ba4c30bffd986ca607cefe26895c3b3bd4b58cd11038fdd18f0b","source":{"kind":"arxiv","id":"1209.3466","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3466","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3466v1","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3466","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"53EHVBSJ6O5E","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"53EHVBSJ6O5EYMF7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"53EHVBSJ","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:53EHVBSJ6O5EYMF77WMGZJQHZ3","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-16T08:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"0be252d6042f2a77796ca9ebc80c95b71c7f8c355e0e2b1e9109b9129c3d1236","abstract_canon_sha256":"051f66badd9635c685612648de1c6b03ac6aa19289617a530cb2616774e51d33"},"schema_version":"1.0"},"canonical_sha256":"eec87a8649f3ba4c30bffd986ca607cefe26895c3b3bd4b58cd11038fdd18f0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:11.005845Z","signature_b64":"m3RK4mxarSCdb94L7tHiDef1p7XJ8f+VdFAIGUFtk6kLg3BljNo+HxyDbM60A2B04LsqYKSabDRNJX/7gefjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eec87a8649f3ba4c30bffd986ca607cefe26895c3b3bd4b58cd11038fdd18f0b","last_reissued_at":"2026-05-18T02:20:11.005352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:11.005352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3466","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":"2026-05-18T02:20:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7nyNB4rAAM0LZJ+FzEGNdXJ6DdFGQTI2G9AERavSQSmEFDIzEJd5IUNxbHoECFOzkeQFnX1A4ScDGFRmMZmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:42:44.544708Z"},"content_sha256":"0cb369d55c8865e4b6bec6ff23fcc8515ebf52c72af7c38ced9088938b9ef295","schema_version":"1.0","event_id":"sha256:0cb369d55c8865e4b6bec6ff23fcc8515ebf52c72af7c38ced9088938b9ef295"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:53EHVBSJ6O5EYMF77WMGZJQHZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hierarchical logistic equation to describe the dynamical behavior of penetration rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Hiroe Minagawa, Michiko Chiba, Tohru Tashiro","submitted_at":"2012-09-16T08:30:06Z","abstract_excerpt":"We propose a hierarchical logistic equation as a model to describe the dynamical behavior of a penetration rate of a prevalent stuff. In this model, a memory, how many people who already possess it a person who does not process it yet met, is considered, which does not exist in the logistic model. As an application, we apply this model to iPod sales data, and find that this model can approximate the data much better than the logistic equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3466","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":"2026-05-18T02:20:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lEegCw29W147rrCgARp1luaMWYmo4iy0o+WGtMKeE7/qFIo8ZbTLbuLORI8lkqEmMCIGRgvMFyhOa5eOYEeKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:42:44.545039Z"},"content_sha256":"2db1caa3111be8353c33ba42237f7db83256e9df16f5bed1162db1ce093757fc","schema_version":"1.0","event_id":"sha256:2db1caa3111be8353c33ba42237f7db83256e9df16f5bed1162db1ce093757fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53EHVBSJ6O5EYMF77WMGZJQHZ3/bundle.json","state_url":"https://pith.science/pith/53EHVBSJ6O5EYMF77WMGZJQHZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53EHVBSJ6O5EYMF77WMGZJQHZ3/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":"2026-06-28T18:42:44Z","links":{"resolver":"https://pith.science/pith/53EHVBSJ6O5EYMF77WMGZJQHZ3","bundle":"https://pith.science/pith/53EHVBSJ6O5EYMF77WMGZJQHZ3/bundle.json","state":"https://pith.science/pith/53EHVBSJ6O5EYMF77WMGZJQHZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53EHVBSJ6O5EYMF77WMGZJQHZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:53EHVBSJ6O5EYMF77WMGZJQHZ3","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":"051f66badd9635c685612648de1c6b03ac6aa19289617a530cb2616774e51d33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-16T08:30:06Z","title_canon_sha256":"0be252d6042f2a77796ca9ebc80c95b71c7f8c355e0e2b1e9109b9129c3d1236"},"schema_version":"1.0","source":{"id":"1209.3466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3466","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3466v1","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3466","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"53EHVBSJ6O5E","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"53EHVBSJ6O5EYMF7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"53EHVBSJ","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:2db1caa3111be8353c33ba42237f7db83256e9df16f5bed1162db1ce093757fc","target":"graph","created_at":"2026-05-18T02:20:11Z","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 propose a hierarchical logistic equation as a model to describe the dynamical behavior of a penetration rate of a prevalent stuff. In this model, a memory, how many people who already possess it a person who does not process it yet met, is considered, which does not exist in the logistic model. As an application, we apply this model to iPod sales data, and find that this model can approximate the data much better than the logistic equation.","authors_text":"Hiroe Minagawa, Michiko Chiba, Tohru Tashiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-16T08:30:06Z","title":"Hierarchical logistic equation to describe the dynamical behavior of penetration rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3466","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":"sha256:0cb369d55c8865e4b6bec6ff23fcc8515ebf52c72af7c38ced9088938b9ef295","target":"record","created_at":"2026-05-18T02:20:11Z","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":"051f66badd9635c685612648de1c6b03ac6aa19289617a530cb2616774e51d33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-16T08:30:06Z","title_canon_sha256":"0be252d6042f2a77796ca9ebc80c95b71c7f8c355e0e2b1e9109b9129c3d1236"},"schema_version":"1.0","source":{"id":"1209.3466","kind":"arxiv","version":1}},"canonical_sha256":"eec87a8649f3ba4c30bffd986ca607cefe26895c3b3bd4b58cd11038fdd18f0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eec87a8649f3ba4c30bffd986ca607cefe26895c3b3bd4b58cd11038fdd18f0b","first_computed_at":"2026-05-18T02:20:11.005352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:11.005352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3RK4mxarSCdb94L7tHiDef1p7XJ8f+VdFAIGUFtk6kLg3BljNo+HxyDbM60A2B04LsqYKSabDRNJX/7gefjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:11.005845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cb369d55c8865e4b6bec6ff23fcc8515ebf52c72af7c38ced9088938b9ef295","sha256:2db1caa3111be8353c33ba42237f7db83256e9df16f5bed1162db1ce093757fc"],"state_sha256":"3c2f172459156b84e5cb480324aac818ce73266ea9bb78ffde739382e0fc69bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4UVHBJhMDJFBgrWBJ7b2kwoqBibtSUAaV0MzeQLvn7OsSY5qqjYa2EEUoa9RWfmgss3rO4w3FGU1DxWms8agCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T18:42:44.547004Z","bundle_sha256":"2c9a269426c60c78ac84057c5ed13e59544dab81b1227222e70fb719ea93c74d"}}