{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FUAW6S6E3XIWSPX5ST5IBWDQIP","short_pith_number":"pith:FUAW6S6E","canonical_record":{"source":{"id":"1011.2870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-12T10:08:35Z","cross_cats_sorted":["math.MP","physics.data-an","physics.plasm-ph"],"title_canon_sha256":"a8ac03f856eecad635d6ae988fc4c846783abeb89270fbd369b9bdc1626afcbd","abstract_canon_sha256":"e43b30e67bbd42a85a39d70f5cfbc30c7db3823cbb30093afff40b9db1467785"},"schema_version":"1.0"},"canonical_sha256":"2d016f4bc4ddd1693efd94fa80d87043fd48e165724e9fa24880fa7acfc7916c","source":{"kind":"arxiv","id":"1011.2870","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2870","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2870v2","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2870","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"FUAW6S6E3XIW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FUAW6S6E3XIWSPX5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FUAW6S6E","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FUAW6S6E3XIWSPX5ST5IBWDQIP","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-12T10:08:35Z","cross_cats_sorted":["math.MP","physics.data-an","physics.plasm-ph"],"title_canon_sha256":"a8ac03f856eecad635d6ae988fc4c846783abeb89270fbd369b9bdc1626afcbd","abstract_canon_sha256":"e43b30e67bbd42a85a39d70f5cfbc30c7db3823cbb30093afff40b9db1467785"},"schema_version":"1.0"},"canonical_sha256":"2d016f4bc4ddd1693efd94fa80d87043fd48e165724e9fa24880fa7acfc7916c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:33.616361Z","signature_b64":"FQcdVCIyAnF2a1/xY4KkF0l0qcq6UxOtH3e/FwEhOYW8d/xNmhN/8h0QyprVXOrqG5r1b+bd5Ivffzn2RsmDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d016f4bc4ddd1693efd94fa80d87043fd48e165724e9fa24880fa7acfc7916c","last_reissued_at":"2026-05-18T03:25:33.615702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:33.615702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2870","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0hmosV0dy78X98nswLPWITRZ1KuRn+KocfEPr/QkPXL3BEIFVyWPH3aPHphyBMNRh4EURp/T1ARm0WBYcwdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:01:43.337225Z"},"content_sha256":"50abe5ce80f7e6226d2e1668b1912b8719bb599e877f12cf35f2469d13cb2494","schema_version":"1.0","event_id":"sha256:50abe5ce80f7e6226d2e1668b1912b8719bb599e877f12cf35f2469d13cb2494"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FUAW6S6E3XIWSPX5ST5IBWDQIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear theory and violent relaxation in long-range systems: a test case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.data-an","physics.plasm-ph"],"primary_cat":"math-ph","authors_text":"Marie-Christine Firpo, Wahb Ettoumi","submitted_at":"2010-11-12T10:08:35Z","abstract_excerpt":"In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N \\rightarrow \\infty$, approach, the growth rates are finally derived without restrictin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2870","kind":"arxiv","version":2},"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":"2026-05-18T03:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KdnDLB/3OjAkapyifrlJLxv5t+9g3AKg6KFR76XzXJn9av5N7CbjGX5iVeJ2qupDkpW7Ob90yDblKNJ7QQp7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:01:43.337713Z"},"content_sha256":"28988ed9b96aa2a01ba9fc76ec82bdb175a127fedc467e4b59eaf50bb9568ff0","schema_version":"1.0","event_id":"sha256:28988ed9b96aa2a01ba9fc76ec82bdb175a127fedc467e4b59eaf50bb9568ff0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUAW6S6E3XIWSPX5ST5IBWDQIP/bundle.json","state_url":"https://pith.science/pith/FUAW6S6E3XIWSPX5ST5IBWDQIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUAW6S6E3XIWSPX5ST5IBWDQIP/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":"2026-06-24T06:01:43Z","links":{"resolver":"https://pith.science/pith/FUAW6S6E3XIWSPX5ST5IBWDQIP","bundle":"https://pith.science/pith/FUAW6S6E3XIWSPX5ST5IBWDQIP/bundle.json","state":"https://pith.science/pith/FUAW6S6E3XIWSPX5ST5IBWDQIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUAW6S6E3XIWSPX5ST5IBWDQIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FUAW6S6E3XIWSPX5ST5IBWDQIP","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":"e43b30e67bbd42a85a39d70f5cfbc30c7db3823cbb30093afff40b9db1467785","cross_cats_sorted":["math.MP","physics.data-an","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-12T10:08:35Z","title_canon_sha256":"a8ac03f856eecad635d6ae988fc4c846783abeb89270fbd369b9bdc1626afcbd"},"schema_version":"1.0","source":{"id":"1011.2870","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2870","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2870v2","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2870","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"FUAW6S6E3XIW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FUAW6S6E3XIWSPX5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FUAW6S6E","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:28988ed9b96aa2a01ba9fc76ec82bdb175a127fedc467e4b59eaf50bb9568ff0","target":"graph","created_at":"2026-05-18T03:25:33Z","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":"In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N \\rightarrow \\infty$, approach, the growth rates are finally derived without restrictin","authors_text":"Marie-Christine Firpo, Wahb Ettoumi","cross_cats":["math.MP","physics.data-an","physics.plasm-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-12T10:08:35Z","title":"Linear theory and violent relaxation in long-range systems: a test case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2870","kind":"arxiv","version":2},"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":"sha256:50abe5ce80f7e6226d2e1668b1912b8719bb599e877f12cf35f2469d13cb2494","target":"record","created_at":"2026-05-18T03:25:33Z","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":"e43b30e67bbd42a85a39d70f5cfbc30c7db3823cbb30093afff40b9db1467785","cross_cats_sorted":["math.MP","physics.data-an","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-12T10:08:35Z","title_canon_sha256":"a8ac03f856eecad635d6ae988fc4c846783abeb89270fbd369b9bdc1626afcbd"},"schema_version":"1.0","source":{"id":"1011.2870","kind":"arxiv","version":2}},"canonical_sha256":"2d016f4bc4ddd1693efd94fa80d87043fd48e165724e9fa24880fa7acfc7916c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d016f4bc4ddd1693efd94fa80d87043fd48e165724e9fa24880fa7acfc7916c","first_computed_at":"2026-05-18T03:25:33.615702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:33.615702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQcdVCIyAnF2a1/xY4KkF0l0qcq6UxOtH3e/FwEhOYW8d/xNmhN/8h0QyprVXOrqG5r1b+bd5Ivffzn2RsmDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:33.616361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2870","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50abe5ce80f7e6226d2e1668b1912b8719bb599e877f12cf35f2469d13cb2494","sha256:28988ed9b96aa2a01ba9fc76ec82bdb175a127fedc467e4b59eaf50bb9568ff0"],"state_sha256":"837dff7ea0116c6fd2bb76a588909f04eba115055e15ffc346849aba088694bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gb2IyzhQKQ0P4jlYknPLDT9OzgR7fVA0218sK6eNiU4t0L92oYqMpRSb55VjlZDDf91382j3vmP2Q3GGU1sTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:01:43.340291Z","bundle_sha256":"a2617d291c51a9d8185e6393166bc52aa6aec5b1b59ffb750386a77421087d7f"}}