{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:FXALPHAMLTMOQI4QUCXKVNQSUH","short_pith_number":"pith:FXALPHAM","canonical_record":{"source":{"id":"cs/0605073","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2006-05-17T12:02:01Z","cross_cats_sorted":["cs.CE","math.IT"],"title_canon_sha256":"b26ce9bd18f2546eebc7ac1c8672a530649e6a76a4204965246f171448d86eda","abstract_canon_sha256":"a60aa041b8f678067a6f993c5d7b41ef98a5ea6593f3712673acebcacf640444"},"schema_version":"1.0"},"canonical_sha256":"2dc0b79c0c5cd8e82390a0aeaab612a1daf75b4fb51d554e32c2a120a48d99fe","source":{"kind":"arxiv","id":"cs/0605073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0605073","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0605073v1","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0605073","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"FXALPHAMLTMO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"FXALPHAMLTMOQI4Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"FXALPHAM","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:FXALPHAMLTMOQI4QUCXKVNQSUH","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0605073","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2006-05-17T12:02:01Z","cross_cats_sorted":["cs.CE","math.IT"],"title_canon_sha256":"b26ce9bd18f2546eebc7ac1c8672a530649e6a76a4204965246f171448d86eda","abstract_canon_sha256":"a60aa041b8f678067a6f993c5d7b41ef98a5ea6593f3712673acebcacf640444"},"schema_version":"1.0"},"canonical_sha256":"2dc0b79c0c5cd8e82390a0aeaab612a1daf75b4fb51d554e32c2a120a48d99fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:05.264518Z","signature_b64":"PoG8g/ufdQEfAZ7VhscNlWwKp1+WAyay6TutauSLQyIfOvzJ+zVguw/r6QF68snY56iTJeUAA2KwiMs2DGOJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dc0b79c0c5cd8e82390a0aeaab612a1daf75b4fb51d554e32c2a120a48d99fe","last_reissued_at":"2026-05-18T03:58:05.263883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:05.263883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0605073","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":"2026-05-18T03:58:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XdjpxDmZv4veIbfdSbHYlzopzUNvpFr7/J3/YTvfKEBraD8NVH26evKeNuNXTB/i/oyaRCaol2OsByJoq+tMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:07:14.188487Z"},"content_sha256":"bb091e99e5893a90cbebbeb995b2e56e5876b825275939d41d73943908cb7643","schema_version":"1.0","event_id":"sha256:bb091e99e5893a90cbebbeb995b2e56e5876b825275939d41d73943908cb7643"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:FXALPHAMLTMOQI4QUCXKVNQSUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic Properties and Covariance Functions of a New Class of Generalized Gibbs Random Fields","license":"","headline":"","cross_cats":["cs.CE","math.IT"],"primary_cat":"cs.IT","authors_text":"Dionissios T. Hristopulos, Samuel Elogne","submitted_at":"2006-05-17T12:02:01Z","abstract_excerpt":"Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions and a small set of free parameters (interaction couplings). This paper focuses on the FGC-SSRF model, which is defined on the Euclidean space $\\mathbb{R}^{d}$ by means of interactions proportional to the squares of the field realizations, as well as their gradient and curvature. The permissibility criteria of FGC-SSRFs are extended by considering the impact o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0605073","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":"2026-05-18T03:58:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4SV+k4HQwg05Cj7nsCdFOn80OrFKHtbl8s8COL2bIjsSmdHdKWJtCS0r9iNnw7qEdQ8hUsKhA/Ua30Y1dYYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:07:14.188840Z"},"content_sha256":"36276501bcd14b819f74632902babc28d5d2ce666304829a064232267aa0f6ce","schema_version":"1.0","event_id":"sha256:36276501bcd14b819f74632902babc28d5d2ce666304829a064232267aa0f6ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXALPHAMLTMOQI4QUCXKVNQSUH/bundle.json","state_url":"https://pith.science/pith/FXALPHAMLTMOQI4QUCXKVNQSUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXALPHAMLTMOQI4QUCXKVNQSUH/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":"2026-06-09T16:07:14Z","links":{"resolver":"https://pith.science/pith/FXALPHAMLTMOQI4QUCXKVNQSUH","bundle":"https://pith.science/pith/FXALPHAMLTMOQI4QUCXKVNQSUH/bundle.json","state":"https://pith.science/pith/FXALPHAMLTMOQI4QUCXKVNQSUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXALPHAMLTMOQI4QUCXKVNQSUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:FXALPHAMLTMOQI4QUCXKVNQSUH","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":"a60aa041b8f678067a6f993c5d7b41ef98a5ea6593f3712673acebcacf640444","cross_cats_sorted":["cs.CE","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2006-05-17T12:02:01Z","title_canon_sha256":"b26ce9bd18f2546eebc7ac1c8672a530649e6a76a4204965246f171448d86eda"},"schema_version":"1.0","source":{"id":"cs/0605073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0605073","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0605073v1","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0605073","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"FXALPHAMLTMO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"FXALPHAMLTMOQI4Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"FXALPHAM","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:36276501bcd14b819f74632902babc28d5d2ce666304829a064232267aa0f6ce","target":"graph","created_at":"2026-05-18T03:58:05Z","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":"Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions and a small set of free parameters (interaction couplings). This paper focuses on the FGC-SSRF model, which is defined on the Euclidean space $\\mathbb{R}^{d}$ by means of interactions proportional to the squares of the field realizations, as well as their gradient and curvature. The permissibility criteria of FGC-SSRFs are extended by considering the impact o","authors_text":"Dionissios T. Hristopulos, Samuel Elogne","cross_cats":["cs.CE","math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2006-05-17T12:02:01Z","title":"Analytic Properties and Covariance Functions of a New Class of Generalized Gibbs Random Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0605073","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:bb091e99e5893a90cbebbeb995b2e56e5876b825275939d41d73943908cb7643","target":"record","created_at":"2026-05-18T03:58:05Z","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":"a60aa041b8f678067a6f993c5d7b41ef98a5ea6593f3712673acebcacf640444","cross_cats_sorted":["cs.CE","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2006-05-17T12:02:01Z","title_canon_sha256":"b26ce9bd18f2546eebc7ac1c8672a530649e6a76a4204965246f171448d86eda"},"schema_version":"1.0","source":{"id":"cs/0605073","kind":"arxiv","version":1}},"canonical_sha256":"2dc0b79c0c5cd8e82390a0aeaab612a1daf75b4fb51d554e32c2a120a48d99fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dc0b79c0c5cd8e82390a0aeaab612a1daf75b4fb51d554e32c2a120a48d99fe","first_computed_at":"2026-05-18T03:58:05.263883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:05.263883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PoG8g/ufdQEfAZ7VhscNlWwKp1+WAyay6TutauSLQyIfOvzJ+zVguw/r6QF68snY56iTJeUAA2KwiMs2DGOJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:05.264518Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0605073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb091e99e5893a90cbebbeb995b2e56e5876b825275939d41d73943908cb7643","sha256:36276501bcd14b819f74632902babc28d5d2ce666304829a064232267aa0f6ce"],"state_sha256":"22d51dae7524ed73ef3fbb03d3b1d5a91f8e09f04b454e76c7ff4761bacd282c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2/lGEeRNzbXtn13VZCqg1bru1jaLNTApn/B4NnGN2/cBAeM0jCrUg3DCtUAaI/t6PSPrKsu61u8BJz4w1QX4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:07:14.190913Z","bundle_sha256":"c5b48a72d092e3cda5e37f7c17289a13b30198276e5eb7407690baa400a6f376"}}