{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z7LEJIHY4FBVPNACVIFGNEK5DF","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":"09b297fb51134e8c13a67807eeee8e535d3dd1316830ebb0ead8b778311139f2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-03T03:42:26Z","title_canon_sha256":"9020d780d3f0ed66a6369ca5d9734e42b0abddfdad47da18ec58d433f38c0e20"},"schema_version":"1.0","source":{"id":"2608.01650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01650","created_at":"2026-08-04T02:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01650v1","created_at":"2026-08-04T02:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01650","created_at":"2026-08-04T02:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"Z7LEJIHY4FBV","created_at":"2026-08-04T02:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"Z7LEJIHY4FBVPNAC","created_at":"2026-08-04T02:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"Z7LEJIHY","created_at":"2026-08-04T02:06:20Z"}],"graph_snapshots":[{"event_id":"sha256:49c5be8d16382148bebab16564f5d1df162ed739afe4972e5321adc5136320b1","target":"graph","created_at":"2026-08-04T02:06:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.01650/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a rigorous mathematical framework in which the continuous space-time coordinate continuum and self-regulating field dynamics are derived from non-local, periodic primitives termed primal wave fields. Traditional continuum mechanics models physical phenomena over a pre-existing background of real numbers ($R$), an approach that inherently introduces unphysical, localized mathematical divergences (singularities) when computing point-like field interactions. We resolve these foundational vulnerabilities by constructing a three-tiered algebraic architecture - the base set $W_","authors_text":"Terence R. Smith","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-03T03:42:26Z","title":"Constructing Self-Regulating Field Theoriesfrom Primal Wave Fields without Background Manifolds:The Emergence of the Coordinate Continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01650","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":"sha256:1d889e982f0d4ac6da807b3eed910e3da91cfcdc1e019fc9e618908ec1efb4cd","target":"record","created_at":"2026-08-04T02:06:20Z","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":"09b297fb51134e8c13a67807eeee8e535d3dd1316830ebb0ead8b778311139f2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-03T03:42:26Z","title_canon_sha256":"9020d780d3f0ed66a6369ca5d9734e42b0abddfdad47da18ec58d433f38c0e20"},"schema_version":"1.0","source":{"id":"2608.01650","kind":"arxiv","version":1}},"canonical_sha256":"cfd644a0f8e14357b402aa0a66915d197b9f169b11c66a9e4fc2f3c592958429","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfd644a0f8e14357b402aa0a66915d197b9f169b11c66a9e4fc2f3c592958429","first_computed_at":"2026-08-04T02:06:20.126478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:06:20.126478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7jg3GaokKR0tTaE3wIrDDo2clNWhFVgtqtx4mJS76om9j4jmQ9rkoV8ZhIostf+aL2/9TlLQksdm8LQ8wscbCQ==","signature_status":"signed_v1","signed_at":"2026-08-04T02:06:20.128263Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.01650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d889e982f0d4ac6da807b3eed910e3da91cfcdc1e019fc9e618908ec1efb4cd","sha256:49c5be8d16382148bebab16564f5d1df162ed739afe4972e5321adc5136320b1"],"state_sha256":"316fa359a23e159218055d3abd64c673a8437b3554d343b40944fb4c8b8831e2"}