{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7IFYR3TPJRWH5ECVHD4WM3GQDZ","short_pith_number":"pith:7IFYR3TP","canonical_record":{"source":{"id":"1101.5888","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-31T09:55:24Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"ff58dcdb22a599acc8f945901fa934d0b6c84026e7813c4f15445adc928ce082","abstract_canon_sha256":"343ba9cc81cfe56828f44b01d17e28aa0e6ad46de7dd49016c37c0b6e5138b24"},"schema_version":"1.0"},"canonical_sha256":"fa0b88ee6f4c6c7e905538f9666cd01e545ca79252945a381f5b03985babaa27","source":{"kind":"arxiv","id":"1101.5888","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5888","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5888v4","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5888","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"7IFYR3TPJRWH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7IFYR3TPJRWH5ECV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7IFYR3TP","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7IFYR3TPJRWH5ECVHD4WM3GQDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1101.5888","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-31T09:55:24Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"ff58dcdb22a599acc8f945901fa934d0b6c84026e7813c4f15445adc928ce082","abstract_canon_sha256":"343ba9cc81cfe56828f44b01d17e28aa0e6ad46de7dd49016c37c0b6e5138b24"},"schema_version":"1.0"},"canonical_sha256":"fa0b88ee6f4c6c7e905538f9666cd01e545ca79252945a381f5b03985babaa27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:41.848104Z","signature_b64":"M07CUyol/hneDAEZxx7hnho0k/tTF4aAHAZgE9o75CQBEuU+E20TXpyP/fxPncTiH4p+FhkxboAQcHsMFcTYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa0b88ee6f4c6c7e905538f9666cd01e545ca79252945a381f5b03985babaa27","last_reissued_at":"2026-05-18T02:22:41.847536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:41.847536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.5888","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KjVhoPHeT2xBs3EFAv4QEcQ0S0G+0UPXf7jMXLpy67ZN9YQG7TMyQTLy4FTy78+TtO0F52IHWQVlhKTTQg4YDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:27:00.822882Z"},"content_sha256":"808726877e209894cbf386448d591b6a438d69b804fef64de37e780f13e0efba","schema_version":"1.0","event_id":"sha256:808726877e209894cbf386448d591b6a438d69b804fef64de37e780f13e0efba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7IFYR3TPJRWH5ECVHD4WM3GQDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Didier Sornette, Ryohei Hisano, Takayuki Mizuno","submitted_at":"2011-01-31T09:55:24Z","abstract_excerpt":"Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional growth, and (ii) birth and death processes, leads to a generic power-law distribution with an exponent that depends on the characteristics of each ingredient. Here, we report the first complete empirica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5888","kind":"arxiv","version":4},"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":"2026-05-18T02:22:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vztuSoyYvxVYG+rLPM1AV1T9NWv0Ycx/m1hGQqNFbVMiHyahmBKu9TZ+1Ds5icOCBFb2eDShi5xAlKPWB96aCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:27:00.823216Z"},"content_sha256":"8bf7b9c9ad948aacb27ed61241f5c97427ab7250050f3aee69410996a6a73a87","schema_version":"1.0","event_id":"sha256:8bf7b9c9ad948aacb27ed61241f5c97427ab7250050f3aee69410996a6a73a87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IFYR3TPJRWH5ECVHD4WM3GQDZ/bundle.json","state_url":"https://pith.science/pith/7IFYR3TPJRWH5ECVHD4WM3GQDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IFYR3TPJRWH5ECVHD4WM3GQDZ/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":"2026-06-21T23:27:00Z","links":{"resolver":"https://pith.science/pith/7IFYR3TPJRWH5ECVHD4WM3GQDZ","bundle":"https://pith.science/pith/7IFYR3TPJRWH5ECVHD4WM3GQDZ/bundle.json","state":"https://pith.science/pith/7IFYR3TPJRWH5ECVHD4WM3GQDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IFYR3TPJRWH5ECVHD4WM3GQDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7IFYR3TPJRWH5ECVHD4WM3GQDZ","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":"343ba9cc81cfe56828f44b01d17e28aa0e6ad46de7dd49016c37c0b6e5138b24","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-31T09:55:24Z","title_canon_sha256":"ff58dcdb22a599acc8f945901fa934d0b6c84026e7813c4f15445adc928ce082"},"schema_version":"1.0","source":{"id":"1101.5888","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5888","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5888v4","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5888","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"7IFYR3TPJRWH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7IFYR3TPJRWH5ECV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7IFYR3TP","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:8bf7b9c9ad948aacb27ed61241f5c97427ab7250050f3aee69410996a6a73a87","target":"graph","created_at":"2026-05-18T02:22:41Z","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":"Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional growth, and (ii) birth and death processes, leads to a generic power-law distribution with an exponent that depends on the characteristics of each ingredient. Here, we report the first complete empirica","authors_text":"Didier Sornette, Ryohei Hisano, Takayuki Mizuno","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-31T09:55:24Z","title":"Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5888","kind":"arxiv","version":4},"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":"sha256:808726877e209894cbf386448d591b6a438d69b804fef64de37e780f13e0efba","target":"record","created_at":"2026-05-18T02:22:41Z","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":"343ba9cc81cfe56828f44b01d17e28aa0e6ad46de7dd49016c37c0b6e5138b24","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-31T09:55:24Z","title_canon_sha256":"ff58dcdb22a599acc8f945901fa934d0b6c84026e7813c4f15445adc928ce082"},"schema_version":"1.0","source":{"id":"1101.5888","kind":"arxiv","version":4}},"canonical_sha256":"fa0b88ee6f4c6c7e905538f9666cd01e545ca79252945a381f5b03985babaa27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa0b88ee6f4c6c7e905538f9666cd01e545ca79252945a381f5b03985babaa27","first_computed_at":"2026-05-18T02:22:41.847536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:41.847536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M07CUyol/hneDAEZxx7hnho0k/tTF4aAHAZgE9o75CQBEuU+E20TXpyP/fxPncTiH4p+FhkxboAQcHsMFcTYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:41.848104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5888","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:808726877e209894cbf386448d591b6a438d69b804fef64de37e780f13e0efba","sha256:8bf7b9c9ad948aacb27ed61241f5c97427ab7250050f3aee69410996a6a73a87"],"state_sha256":"077ac49c8b501eb47695bc9e4a7ae75f895f6a10afdf995d53ac0a9ab70af62b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PX7JLsrrVvGllX52ew5ttTARQX3dxAEA5Jxh8p3bP/kbu16SAUAsixV22/B1NOyfiYuxbZSZBo2hvmrRGcWdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:27:00.825008Z","bundle_sha256":"e358ca93cc142007be053767c0aba077c225f3cefae664d8f845a56da1bb94c1"}}