{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7L4L43FWZC3E36AV3ALBRLTRMV","short_pith_number":"pith:7L4L43FW","canonical_record":{"source":{"id":"1205.6559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-30T07:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"bf021cfac84b6146562daa6fec489dd6f8702f3effe5eec7f1e3f7a7127ff2e6","abstract_canon_sha256":"037eeb91384e63de4555ed28b3be94a6e7c10b24bda0f2bbce6a121ea1a3e5ea"},"schema_version":"1.0"},"canonical_sha256":"faf8be6cb6c8b64df815d81618ae71655f5b5dca33fb16c4cacdf9ed69468c14","source":{"kind":"arxiv","id":"1205.6559","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6559","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6559v1","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6559","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"7L4L43FWZC3E","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7L4L43FWZC3E36AV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7L4L43FW","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7L4L43FWZC3E36AV3ALBRLTRMV","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-30T07:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"bf021cfac84b6146562daa6fec489dd6f8702f3effe5eec7f1e3f7a7127ff2e6","abstract_canon_sha256":"037eeb91384e63de4555ed28b3be94a6e7c10b24bda0f2bbce6a121ea1a3e5ea"},"schema_version":"1.0"},"canonical_sha256":"faf8be6cb6c8b64df815d81618ae71655f5b5dca33fb16c4cacdf9ed69468c14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:31.626980Z","signature_b64":"s0oyuK+YueEfixxd1i388lLXFuouc7s1hTueEM+FZQWhXjdZvOvPbp4psM0hM2+sFIC+yrXDXYMKzfhlLNY5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faf8be6cb6c8b64df815d81618ae71655f5b5dca33fb16c4cacdf9ed69468c14","last_reissued_at":"2026-05-17T23:41:31.626327Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:31.626327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6559","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":"2026-05-17T23:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ad+FHtFrOtIqdc4Ll8utDAkfhtT5WSYFXBf6CJBfMKFsSXEqVznXJp8LlEU6od2MKseXtKbSV15VVsGZjX9DAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:17:47.667528Z"},"content_sha256":"5dcdd8c2946444f648a8663f053ed36233a6dab12cec3a35d95028045525917a","schema_version":"1.0","event_id":"sha256:5dcdd8c2946444f648a8663f053ed36233a6dab12cec3a35d95028045525917a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7L4L43FWZC3E36AV3ALBRLTRMV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On exponential growth for a certain class of linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nobuo Yoshida, Ryoki Fukushima","submitted_at":"2012-05-30T07:07:25Z","abstract_excerpt":"We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we show that the total mass of the process grows exponentially in time whenever it survives. More precisely, we prove that there exists an open path, oriented in time, along which the mass grows exponentially fast."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6559","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":"2026-05-17T23:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SwJOlHAWC0wpIWFuNEwzrJgXUiRSMGzAqGKzsIDicfMVh4ootTtgVegPhWX31Rh2KmLy0pwEKteKvpQ+CLslBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:17:47.667861Z"},"content_sha256":"378113c45454fe5b1d88b779154ea8427009c169e838d32c74e26d0bee21d918","schema_version":"1.0","event_id":"sha256:378113c45454fe5b1d88b779154ea8427009c169e838d32c74e26d0bee21d918"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7L4L43FWZC3E36AV3ALBRLTRMV/bundle.json","state_url":"https://pith.science/pith/7L4L43FWZC3E36AV3ALBRLTRMV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7L4L43FWZC3E36AV3ALBRLTRMV/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":"2026-06-07T10:17:47Z","links":{"resolver":"https://pith.science/pith/7L4L43FWZC3E36AV3ALBRLTRMV","bundle":"https://pith.science/pith/7L4L43FWZC3E36AV3ALBRLTRMV/bundle.json","state":"https://pith.science/pith/7L4L43FWZC3E36AV3ALBRLTRMV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7L4L43FWZC3E36AV3ALBRLTRMV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7L4L43FWZC3E36AV3ALBRLTRMV","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":"037eeb91384e63de4555ed28b3be94a6e7c10b24bda0f2bbce6a121ea1a3e5ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-30T07:07:25Z","title_canon_sha256":"bf021cfac84b6146562daa6fec489dd6f8702f3effe5eec7f1e3f7a7127ff2e6"},"schema_version":"1.0","source":{"id":"1205.6559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6559","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6559v1","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6559","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"7L4L43FWZC3E","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7L4L43FWZC3E36AV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7L4L43FW","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:378113c45454fe5b1d88b779154ea8427009c169e838d32c74e26d0bee21d918","target":"graph","created_at":"2026-05-17T23:41:31Z","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 a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we show that the total mass of the process grows exponentially in time whenever it survives. More precisely, we prove that there exists an open path, oriented in time, along which the mass grows exponentially fast.","authors_text":"Nobuo Yoshida, Ryoki Fukushima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-30T07:07:25Z","title":"On exponential growth for a certain class of linear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6559","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":"sha256:5dcdd8c2946444f648a8663f053ed36233a6dab12cec3a35d95028045525917a","target":"record","created_at":"2026-05-17T23:41:31Z","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":"037eeb91384e63de4555ed28b3be94a6e7c10b24bda0f2bbce6a121ea1a3e5ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-30T07:07:25Z","title_canon_sha256":"bf021cfac84b6146562daa6fec489dd6f8702f3effe5eec7f1e3f7a7127ff2e6"},"schema_version":"1.0","source":{"id":"1205.6559","kind":"arxiv","version":1}},"canonical_sha256":"faf8be6cb6c8b64df815d81618ae71655f5b5dca33fb16c4cacdf9ed69468c14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faf8be6cb6c8b64df815d81618ae71655f5b5dca33fb16c4cacdf9ed69468c14","first_computed_at":"2026-05-17T23:41:31.626327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:31.626327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s0oyuK+YueEfixxd1i388lLXFuouc7s1hTueEM+FZQWhXjdZvOvPbp4psM0hM2+sFIC+yrXDXYMKzfhlLNY5Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:31.626980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dcdd8c2946444f648a8663f053ed36233a6dab12cec3a35d95028045525917a","sha256:378113c45454fe5b1d88b779154ea8427009c169e838d32c74e26d0bee21d918"],"state_sha256":"db39dbea1a37aa7303337769aede1eb41aaace9542e055c6e4b2f0f1838541e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rjJbqPNdkcu2svpXRIyzscfBFqnxdQ3Ufb15CwPT4wH8Dl53U1CX99F92LyuLma+2Kmj/fH/MENvKNdBlw5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:17:47.669833Z","bundle_sha256":"b1bcdbf8c1fcbdbdd3cfff4d41968a2ee545b2b262c9cb2d8944386d8158c772"}}