{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:GKRPC2KKBBPVJHGTJMCWA6DP66","short_pith_number":"pith:GKRPC2KK","canonical_record":{"source":{"id":"astro-ph/9803187","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1998-03-17T00:00:53Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"5d090bb2726b6df2ef2290bcc5db3dde352525c6be0dc6fe884532a78186dbaa","abstract_canon_sha256":"22b37925c67d02baca9001bb18f3be74c2826f12453553a4b30a5d2cf89b7e38"},"schema_version":"1.0"},"canonical_sha256":"32a2f1694a085f549cd34b0560786ff7a1db0cb9eeab175c0400eee8f797a92b","source":{"kind":"arxiv","id":"astro-ph/9803187","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9803187","created_at":"2026-05-18T04:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9803187v1","created_at":"2026-05-18T04:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9803187","created_at":"2026-05-18T04:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"GKRPC2KKBBPV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"GKRPC2KKBBPVJHGT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"GKRPC2KK","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:GKRPC2KKBBPVJHGTJMCWA6DP66","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/9803187","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1998-03-17T00:00:53Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"5d090bb2726b6df2ef2290bcc5db3dde352525c6be0dc6fe884532a78186dbaa","abstract_canon_sha256":"22b37925c67d02baca9001bb18f3be74c2826f12453553a4b30a5d2cf89b7e38"},"schema_version":"1.0"},"canonical_sha256":"32a2f1694a085f549cd34b0560786ff7a1db0cb9eeab175c0400eee8f797a92b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:40.234454Z","signature_b64":"NzlwGv65j3LBLfxnCsqne2mnW7yj2pwLM8vkF4kXosPhMtLjEPY04+X+m3M4PAuqhpTRSF96uFXUMcyxZXf6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a2f1694a085f549cd34b0560786ff7a1db0cb9eeab175c0400eee8f797a92b","last_reissued_at":"2026-05-18T04:21:40.233862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:40.233862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/9803187","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":"2026-05-18T04:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ZVG4L0YwZ8eQVfXzJYYPFkFsl8I74xZvcjdUoq/EKP+uWx7uG+QD1CNNJTnsWOQla8ATanPkXsyXlGqNngWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:58:57.042081Z"},"content_sha256":"4a405930be0207ae375fb10b83f1b891ce205ca31df117cfa008ffcbb22778c1","schema_version":"1.0","event_id":"sha256:4a405930be0207ae375fb10b83f1b891ce205ca31df117cfa008ffcbb22778c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:GKRPC2KKBBPVJHGTJMCWA6DP66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Dynamical Approach to a Self-similar Universe","license":"","headline":"","cross_cats":["gr-qc","hep-ph","hep-th"],"primary_cat":"astro-ph","authors_text":"E. Abdalla, K. Khodjasteh, N. Afshordi, R. Mohayaee","submitted_at":"1998-03-17T00:00:53Z","abstract_excerpt":"We write a non-relativistic Lagrangian for a hierarchical universe. The equations of motion are solved numerically and the evolution of the fractal dimension is obtained for different initial conditions. We show that our model is homogeneous at the time of the last scattering, but evolves into a self-similar universe with a remarkably constant fractal dimension. We also show that the Hubble law is implied by this model and make an estimate for the age of the universe."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9803187","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":"2026-05-18T04:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeFXM640Y6MYawQ6yJQaFwXgGUr6JMdY/oeecUpiDf643ON2RStAEZKnQtGlVNP5PWkYkVSOJbjZWmxFeanfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:58:57.042436Z"},"content_sha256":"45f3866ee5fb5ea0a78dc40e76e3ac5efb86e476676719689cbba31c92188c12","schema_version":"1.0","event_id":"sha256:45f3866ee5fb5ea0a78dc40e76e3ac5efb86e476676719689cbba31c92188c12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKRPC2KKBBPVJHGTJMCWA6DP66/bundle.json","state_url":"https://pith.science/pith/GKRPC2KKBBPVJHGTJMCWA6DP66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKRPC2KKBBPVJHGTJMCWA6DP66/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":"2026-06-02T02:58:57Z","links":{"resolver":"https://pith.science/pith/GKRPC2KKBBPVJHGTJMCWA6DP66","bundle":"https://pith.science/pith/GKRPC2KKBBPVJHGTJMCWA6DP66/bundle.json","state":"https://pith.science/pith/GKRPC2KKBBPVJHGTJMCWA6DP66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKRPC2KKBBPVJHGTJMCWA6DP66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:GKRPC2KKBBPVJHGTJMCWA6DP66","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":"22b37925c67d02baca9001bb18f3be74c2826f12453553a4b30a5d2cf89b7e38","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"1998-03-17T00:00:53Z","title_canon_sha256":"5d090bb2726b6df2ef2290bcc5db3dde352525c6be0dc6fe884532a78186dbaa"},"schema_version":"1.0","source":{"id":"astro-ph/9803187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9803187","created_at":"2026-05-18T04:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9803187v1","created_at":"2026-05-18T04:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9803187","created_at":"2026-05-18T04:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"GKRPC2KKBBPV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"GKRPC2KKBBPVJHGT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"GKRPC2KK","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:45f3866ee5fb5ea0a78dc40e76e3ac5efb86e476676719689cbba31c92188c12","target":"graph","created_at":"2026-05-18T04:21:40Z","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 write a non-relativistic Lagrangian for a hierarchical universe. The equations of motion are solved numerically and the evolution of the fractal dimension is obtained for different initial conditions. We show that our model is homogeneous at the time of the last scattering, but evolves into a self-similar universe with a remarkably constant fractal dimension. We also show that the Hubble law is implied by this model and make an estimate for the age of the universe.","authors_text":"E. Abdalla, K. Khodjasteh, N. Afshordi, R. Mohayaee","cross_cats":["gr-qc","hep-ph","hep-th"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1998-03-17T00:00:53Z","title":"A Dynamical Approach to a Self-similar Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9803187","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":"sha256:4a405930be0207ae375fb10b83f1b891ce205ca31df117cfa008ffcbb22778c1","target":"record","created_at":"2026-05-18T04:21:40Z","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":"22b37925c67d02baca9001bb18f3be74c2826f12453553a4b30a5d2cf89b7e38","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"1998-03-17T00:00:53Z","title_canon_sha256":"5d090bb2726b6df2ef2290bcc5db3dde352525c6be0dc6fe884532a78186dbaa"},"schema_version":"1.0","source":{"id":"astro-ph/9803187","kind":"arxiv","version":1}},"canonical_sha256":"32a2f1694a085f549cd34b0560786ff7a1db0cb9eeab175c0400eee8f797a92b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a2f1694a085f549cd34b0560786ff7a1db0cb9eeab175c0400eee8f797a92b","first_computed_at":"2026-05-18T04:21:40.233862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:40.233862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NzlwGv65j3LBLfxnCsqne2mnW7yj2pwLM8vkF4kXosPhMtLjEPY04+X+m3M4PAuqhpTRSF96uFXUMcyxZXf6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:40.234454Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9803187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a405930be0207ae375fb10b83f1b891ce205ca31df117cfa008ffcbb22778c1","sha256:45f3866ee5fb5ea0a78dc40e76e3ac5efb86e476676719689cbba31c92188c12"],"state_sha256":"5e3194e837dc0cdf4f0bdce6749969b3976bf6e128954fc452b1fbe07f058245"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfe7+PzKT7BY7rBUJjQb9IEAKVHs7cAEw3z/LbbWOf02oluwsUxZEgHTRxUxCVFlw7hnF6PlFNKH9Kf4kkGzAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:58:57.044373Z","bundle_sha256":"e2d9ddd96719d7722a93d43346949b5794f9c2129f728ccb6efe39273188b887"}}