{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4FM2EQFYXCWORNDMKR55W53DOF","short_pith_number":"pith:4FM2EQFY","canonical_record":{"source":{"id":"1205.6956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-31T10:51:06Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"d5231234c515d4c75ce851aa57641f149699d6857bdb425f0bcdfc29acf27661","abstract_canon_sha256":"e94cfc1f9eb951ae6755b7965e4ad50b895097ad17593cd49a3b5761475126e1"},"schema_version":"1.0"},"canonical_sha256":"e159a240b8b8ace8b46c547bdb77637153cdcc885a7ea51053de4e556f4fefb7","source":{"kind":"arxiv","id":"1205.6956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6956","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6956v1","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6956","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"4FM2EQFYXCWO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4FM2EQFYXCWORNDM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4FM2EQFY","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4FM2EQFYXCWORNDMKR55W53DOF","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-31T10:51:06Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"d5231234c515d4c75ce851aa57641f149699d6857bdb425f0bcdfc29acf27661","abstract_canon_sha256":"e94cfc1f9eb951ae6755b7965e4ad50b895097ad17593cd49a3b5761475126e1"},"schema_version":"1.0"},"canonical_sha256":"e159a240b8b8ace8b46c547bdb77637153cdcc885a7ea51053de4e556f4fefb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:36.530548Z","signature_b64":"Use01PsFo/Cl2KmKAhJGFa99Oh0u/BWpMDddw4RHlBD+tyeuYA/3echE9+3iboZbPAN6zab0H5NWytRsk73nDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e159a240b8b8ace8b46c547bdb77637153cdcc885a7ea51053de4e556f4fefb7","last_reissued_at":"2026-05-18T03:54:36.529950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:36.529950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6956","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":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XEXbZ6gwAw/I/eoKnvbKKPklGo1WZxzH9c1UNQE6c2FlZgDZcSZjxH/bWF+cbTbKn1kyjr4laaE+VWoqpXmJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:23:04.360956Z"},"content_sha256":"14cc16a72d6f90df37787fea7bae072350459062e05321a566878d1e19ab361c","schema_version":"1.0","event_id":"sha256:14cc16a72d6f90df37787fea7bae072350459062e05321a566878d1e19ab361c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4FM2EQFYXCWORNDMKR55W53DOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fine structure of one-dimensional discrete point system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"V. A. Malyshev","submitted_at":"2012-05-31T10:51:06Z","abstract_excerpt":"We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in $N$ and $l$) of finite differences of order $l$. Classical theory of finite differences is extensively used."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6956","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":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8L5cKbN/YmodwGbBst5SXTjahlD6xx2iKrqXOLhT9atgNqiFHl9opmBlWZIHD0qyKzi5hTAl8HhBvXjz2s4vBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:23:04.361300Z"},"content_sha256":"9eb8ab398503768d21b1ee2e6f1e9d2efe4119851b365e34728ba745de5e3553","schema_version":"1.0","event_id":"sha256:9eb8ab398503768d21b1ee2e6f1e9d2efe4119851b365e34728ba745de5e3553"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FM2EQFYXCWORNDMKR55W53DOF/bundle.json","state_url":"https://pith.science/pith/4FM2EQFYXCWORNDMKR55W53DOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FM2EQFYXCWORNDMKR55W53DOF/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":"2026-06-20T08:23:04Z","links":{"resolver":"https://pith.science/pith/4FM2EQFYXCWORNDMKR55W53DOF","bundle":"https://pith.science/pith/4FM2EQFYXCWORNDMKR55W53DOF/bundle.json","state":"https://pith.science/pith/4FM2EQFYXCWORNDMKR55W53DOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FM2EQFYXCWORNDMKR55W53DOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4FM2EQFYXCWORNDMKR55W53DOF","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":"e94cfc1f9eb951ae6755b7965e4ad50b895097ad17593cd49a3b5761475126e1","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-31T10:51:06Z","title_canon_sha256":"d5231234c515d4c75ce851aa57641f149699d6857bdb425f0bcdfc29acf27661"},"schema_version":"1.0","source":{"id":"1205.6956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6956","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6956v1","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6956","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"4FM2EQFYXCWO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4FM2EQFYXCWORNDM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4FM2EQFY","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:9eb8ab398503768d21b1ee2e6f1e9d2efe4119851b365e34728ba745de5e3553","target":"graph","created_at":"2026-05-18T03:54:36Z","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 the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in $N$ and $l$) of finite differences of order $l$. Classical theory of finite differences is extensively used.","authors_text":"V. A. Malyshev","cross_cats":["math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-31T10:51:06Z","title":"Fine structure of one-dimensional discrete point system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6956","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":"sha256:14cc16a72d6f90df37787fea7bae072350459062e05321a566878d1e19ab361c","target":"record","created_at":"2026-05-18T03:54:36Z","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":"e94cfc1f9eb951ae6755b7965e4ad50b895097ad17593cd49a3b5761475126e1","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-31T10:51:06Z","title_canon_sha256":"d5231234c515d4c75ce851aa57641f149699d6857bdb425f0bcdfc29acf27661"},"schema_version":"1.0","source":{"id":"1205.6956","kind":"arxiv","version":1}},"canonical_sha256":"e159a240b8b8ace8b46c547bdb77637153cdcc885a7ea51053de4e556f4fefb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e159a240b8b8ace8b46c547bdb77637153cdcc885a7ea51053de4e556f4fefb7","first_computed_at":"2026-05-18T03:54:36.529950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:36.529950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Use01PsFo/Cl2KmKAhJGFa99Oh0u/BWpMDddw4RHlBD+tyeuYA/3echE9+3iboZbPAN6zab0H5NWytRsk73nDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:36.530548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14cc16a72d6f90df37787fea7bae072350459062e05321a566878d1e19ab361c","sha256:9eb8ab398503768d21b1ee2e6f1e9d2efe4119851b365e34728ba745de5e3553"],"state_sha256":"fd5897e73395db6b497ba579fd0a03c611f025c6ea14195e0aa6bf07f7c00122"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PL/1a0fwtc9zuRuHux35BgVcjc0VPjR6sc3Ve8ZbjLp5i2EntYx+SnQlPXv+WY754Cu33WNJcFUIUdJ0VtlrDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:23:04.363226Z","bundle_sha256":"f165b8b959c0990d7c4c92818acf391ade80bca8ed06ccba08495ee2ffb2e5cb"}}