{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PUGRXIV3X7DUVNGC4676R53XEZ","short_pith_number":"pith:PUGRXIV3","canonical_record":{"source":{"id":"1809.05678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-15T09:12:55Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"3dbfc0ecf55ac97b55633e5a4e72bc82879676b7118d4383aa68fb10959c2fa2","abstract_canon_sha256":"d2a247bfc884ca11ffc39467e338869613d67f56ad127883e2c8b06825f801b9"},"schema_version":"1.0"},"canonical_sha256":"7d0d1ba2bbbfc74ab4c2e7bfe8f7772642aad3e282e4539747f3ceed3e9b881b","source":{"kind":"arxiv","id":"1809.05678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05678","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05678v1","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05678","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"PUGRXIV3X7DU","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PUGRXIV3X7DUVNGC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PUGRXIV3","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PUGRXIV3X7DUVNGC4676R53XEZ","target":"record","payload":{"canonical_record":{"source":{"id":"1809.05678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-15T09:12:55Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"3dbfc0ecf55ac97b55633e5a4e72bc82879676b7118d4383aa68fb10959c2fa2","abstract_canon_sha256":"d2a247bfc884ca11ffc39467e338869613d67f56ad127883e2c8b06825f801b9"},"schema_version":"1.0"},"canonical_sha256":"7d0d1ba2bbbfc74ab4c2e7bfe8f7772642aad3e282e4539747f3ceed3e9b881b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:27.458835Z","signature_b64":"ovTEBWhleSuT1EAKvEKDLbjljbhqvMMU96dykmGV2+13EfmQUAp4GDX1/hhSLN6Fk7LfODWVHN02UkVtWVF2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d0d1ba2bbbfc74ab4c2e7bfe8f7772642aad3e282e4539747f3ceed3e9b881b","last_reissued_at":"2026-05-18T00:05:27.458221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:27.458221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.05678","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":"2026-05-18T00:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1oQrmaGWcq5TLelmawhVo7+ckoGLicxjioulF4nXne9HrzipNdkF10Qx3HiYIVzUrlt5eP+OPrdmJsnTLMkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:28:57.065104Z"},"content_sha256":"5ea40534df55e488a5e5e8b0508889626026f8870ea6c2e6258f24401ff9f6cc","schema_version":"1.0","event_id":"sha256:5ea40534df55e488a5e5e8b0508889626026f8870ea6c2e6258f24401ff9f6cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PUGRXIV3X7DUVNGC4676R53XEZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Alexander B. Balakin, Alexei S. Ilin","submitted_at":"2018-09-15T09:12:55Z","abstract_excerpt":"We study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05678","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":"2026-05-18T00:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yK6S3m+whvUHghwhKDOYAqW/+pdjNYu/jp96tjAEE28KaM3cdbV/y4PNkLNhsXCNfZKe1XjD1OsOqFBaLw3LBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:28:57.065579Z"},"content_sha256":"70575f52e0512433bc819c286210d7b2ac0372a944b14d11cb9390db58d99dfb","schema_version":"1.0","event_id":"sha256:70575f52e0512433bc819c286210d7b2ac0372a944b14d11cb9390db58d99dfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PUGRXIV3X7DUVNGC4676R53XEZ/bundle.json","state_url":"https://pith.science/pith/PUGRXIV3X7DUVNGC4676R53XEZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PUGRXIV3X7DUVNGC4676R53XEZ/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":"2026-07-04T13:28:57Z","links":{"resolver":"https://pith.science/pith/PUGRXIV3X7DUVNGC4676R53XEZ","bundle":"https://pith.science/pith/PUGRXIV3X7DUVNGC4676R53XEZ/bundle.json","state":"https://pith.science/pith/PUGRXIV3X7DUVNGC4676R53XEZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PUGRXIV3X7DUVNGC4676R53XEZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PUGRXIV3X7DUVNGC4676R53XEZ","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":"d2a247bfc884ca11ffc39467e338869613d67f56ad127883e2c8b06825f801b9","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-15T09:12:55Z","title_canon_sha256":"3dbfc0ecf55ac97b55633e5a4e72bc82879676b7118d4383aa68fb10959c2fa2"},"schema_version":"1.0","source":{"id":"1809.05678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05678","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05678v1","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05678","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"PUGRXIV3X7DU","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PUGRXIV3X7DUVNGC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PUGRXIV3","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:70575f52e0512433bc819c286210d7b2ac0372a944b14d11cb9390db58d99dfb","target":"graph","created_at":"2026-05-18T00:05:27Z","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 study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explici","authors_text":"Alexander B. Balakin, Alexei S. Ilin","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-15T09:12:55Z","title":"Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05678","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":"sha256:5ea40534df55e488a5e5e8b0508889626026f8870ea6c2e6258f24401ff9f6cc","target":"record","created_at":"2026-05-18T00:05:27Z","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":"d2a247bfc884ca11ffc39467e338869613d67f56ad127883e2c8b06825f801b9","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-15T09:12:55Z","title_canon_sha256":"3dbfc0ecf55ac97b55633e5a4e72bc82879676b7118d4383aa68fb10959c2fa2"},"schema_version":"1.0","source":{"id":"1809.05678","kind":"arxiv","version":1}},"canonical_sha256":"7d0d1ba2bbbfc74ab4c2e7bfe8f7772642aad3e282e4539747f3ceed3e9b881b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d0d1ba2bbbfc74ab4c2e7bfe8f7772642aad3e282e4539747f3ceed3e9b881b","first_computed_at":"2026-05-18T00:05:27.458221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:27.458221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ovTEBWhleSuT1EAKvEKDLbjljbhqvMMU96dykmGV2+13EfmQUAp4GDX1/hhSLN6Fk7LfODWVHN02UkVtWVF2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:27.458835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.05678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ea40534df55e488a5e5e8b0508889626026f8870ea6c2e6258f24401ff9f6cc","sha256:70575f52e0512433bc819c286210d7b2ac0372a944b14d11cb9390db58d99dfb"],"state_sha256":"2ad0238f9e2818bb1435cf318e98b91f68eab9d4069f835f7d0d31f449e10e47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2kRFmuU0h+2kgNDeBaeV79fFh04jbXg/Gb/GTrB8BSiqIObNKwE2lzQ/nn9qKbaKwakziHJ4wzGi+K66dxbCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T13:28:57.067923Z","bundle_sha256":"f8bf892fe905854f9e5ef3679fb5d6df345092216a10a0baafab7dd41e192753"}}