{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:D3KGEAJXU566QXMYZNXIKU3GTL","short_pith_number":"pith:D3KGEAJX","canonical_record":{"source":{"id":"hep-ph/0004230","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2000-04-25T16:37:16Z","cross_cats_sorted":["astro-ph","gr-qc","hep-th","nlin.PS"],"title_canon_sha256":"2bef3182542c2dcc13ed39e4b80eab55e07733bbba442e749b5f79acceb06fac","abstract_canon_sha256":"c68c891f4281202c4b38e14a4fec33d62cb53a7e21602909003e5a4446366992"},"schema_version":"1.0"},"canonical_sha256":"1ed4620137a77de85d98cb6e8553669afd72ad1ed902ac2d79658cfa2a9cc415","source":{"kind":"arxiv","id":"hep-ph/0004230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0004230","created_at":"2026-05-18T01:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0004230v1","created_at":"2026-05-18T01:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0004230","created_at":"2026-05-18T01:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"D3KGEAJXU566","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"D3KGEAJXU566QXMY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"D3KGEAJX","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:D3KGEAJXU566QXMYZNXIKU3GTL","target":"record","payload":{"canonical_record":{"source":{"id":"hep-ph/0004230","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2000-04-25T16:37:16Z","cross_cats_sorted":["astro-ph","gr-qc","hep-th","nlin.PS"],"title_canon_sha256":"2bef3182542c2dcc13ed39e4b80eab55e07733bbba442e749b5f79acceb06fac","abstract_canon_sha256":"c68c891f4281202c4b38e14a4fec33d62cb53a7e21602909003e5a4446366992"},"schema_version":"1.0"},"canonical_sha256":"1ed4620137a77de85d98cb6e8553669afd72ad1ed902ac2d79658cfa2a9cc415","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:15.671009Z","signature_b64":"iFVi/GAIDaDA7vYKKRFLJRwlQPUs0nYkLDXIl5xnZ7qmi/trTGw6Vc6o59wjBYK+kVM4qvh3LxvJiv6GRzU6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ed4620137a77de85d98cb6e8553669afd72ad1ed902ac2d79658cfa2a9cc415","last_reissued_at":"2026-05-18T01:06:15.670395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:15.670395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-ph/0004230","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":"2026-05-18T01:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+nup1TVguLDiIghza+igb8bUJCuZma/JfwXs9EiZeK1AywBU/OtoAaGE9N6dGfZkQ2psDr542Opzsm6kTQNsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:57:46.639819Z"},"content_sha256":"8ceb4eb670ec5f483d06df9888653a77eeccbc74ea0b93469bd1eec909f70411","schema_version":"1.0","event_id":"sha256:8ceb4eb670ec5f483d06df9888653a77eeccbc74ea0b93469bd1eec909f70411"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:D3KGEAJXU566QXMYZNXIKU3GTL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pattern Formation in the Early Universe","license":"","headline":"","cross_cats":["astro-ph","gr-qc","hep-th","nlin.PS"],"primary_cat":"hep-ph","authors_text":"A. Sornborger, M. Parry","submitted_at":"2000-04-25T16:37:16Z","abstract_excerpt":"Systems that exhibit pattern formation are typically driven and dissipative. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum mechanically if their particles are unstable. Thus, during preheating, a driven-dissipative system exists. We have shown previously that pattern formation can occur in two dimensions in a self-coupled inflaton system undergoing parametric resonance. In this paper, we provide evidence of pattern formation for more realistic initial conditions in both two and three dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0004230","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":"2026-05-18T01:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/5XUX0g/y1jyJMFw3lVIKAUyV9kmRNxGC/pwadiGeqQv3van/3PcUoxMuG12Bc0MaH1SVuVUAAu6w8P8xdTGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:57:46.640171Z"},"content_sha256":"c887dd881dacc587d559d4225a0d28e2924938249a3b76079343b3fd9db7b9e6","schema_version":"1.0","event_id":"sha256:c887dd881dacc587d559d4225a0d28e2924938249a3b76079343b3fd9db7b9e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3KGEAJXU566QXMYZNXIKU3GTL/bundle.json","state_url":"https://pith.science/pith/D3KGEAJXU566QXMYZNXIKU3GTL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3KGEAJXU566QXMYZNXIKU3GTL/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":"2026-06-01T13:57:46Z","links":{"resolver":"https://pith.science/pith/D3KGEAJXU566QXMYZNXIKU3GTL","bundle":"https://pith.science/pith/D3KGEAJXU566QXMYZNXIKU3GTL/bundle.json","state":"https://pith.science/pith/D3KGEAJXU566QXMYZNXIKU3GTL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3KGEAJXU566QXMYZNXIKU3GTL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:D3KGEAJXU566QXMYZNXIKU3GTL","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":"c68c891f4281202c4b38e14a4fec33d62cb53a7e21602909003e5a4446366992","cross_cats_sorted":["astro-ph","gr-qc","hep-th","nlin.PS"],"license":"","primary_cat":"hep-ph","submitted_at":"2000-04-25T16:37:16Z","title_canon_sha256":"2bef3182542c2dcc13ed39e4b80eab55e07733bbba442e749b5f79acceb06fac"},"schema_version":"1.0","source":{"id":"hep-ph/0004230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0004230","created_at":"2026-05-18T01:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0004230v1","created_at":"2026-05-18T01:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0004230","created_at":"2026-05-18T01:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"D3KGEAJXU566","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"D3KGEAJXU566QXMY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"D3KGEAJX","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:c887dd881dacc587d559d4225a0d28e2924938249a3b76079343b3fd9db7b9e6","target":"graph","created_at":"2026-05-18T01:06:15Z","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":"Systems that exhibit pattern formation are typically driven and dissipative. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum mechanically if their particles are unstable. Thus, during preheating, a driven-dissipative system exists. We have shown previously that pattern formation can occur in two dimensions in a self-coupled inflaton system undergoing parametric resonance. In this paper, we provide evidence of pattern formation for more realistic initial conditions in both two and three dimen","authors_text":"A. Sornborger, M. Parry","cross_cats":["astro-ph","gr-qc","hep-th","nlin.PS"],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2000-04-25T16:37:16Z","title":"Pattern Formation in the Early Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0004230","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":"sha256:8ceb4eb670ec5f483d06df9888653a77eeccbc74ea0b93469bd1eec909f70411","target":"record","created_at":"2026-05-18T01:06:15Z","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":"c68c891f4281202c4b38e14a4fec33d62cb53a7e21602909003e5a4446366992","cross_cats_sorted":["astro-ph","gr-qc","hep-th","nlin.PS"],"license":"","primary_cat":"hep-ph","submitted_at":"2000-04-25T16:37:16Z","title_canon_sha256":"2bef3182542c2dcc13ed39e4b80eab55e07733bbba442e749b5f79acceb06fac"},"schema_version":"1.0","source":{"id":"hep-ph/0004230","kind":"arxiv","version":1}},"canonical_sha256":"1ed4620137a77de85d98cb6e8553669afd72ad1ed902ac2d79658cfa2a9cc415","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ed4620137a77de85d98cb6e8553669afd72ad1ed902ac2d79658cfa2a9cc415","first_computed_at":"2026-05-18T01:06:15.670395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:15.670395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iFVi/GAIDaDA7vYKKRFLJRwlQPUs0nYkLDXIl5xnZ7qmi/trTGw6Vc6o59wjBYK+kVM4qvh3LxvJiv6GRzU6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:15.671009Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0004230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ceb4eb670ec5f483d06df9888653a77eeccbc74ea0b93469bd1eec909f70411","sha256:c887dd881dacc587d559d4225a0d28e2924938249a3b76079343b3fd9db7b9e6"],"state_sha256":"0fd58d864bfdf0980bb4f0a75e405774410f461daec4d272d888808d87dce99e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pu/Pzz3tuwaMEcXtpNJ4LviKdGAlobfteeaNv3xLePG7V/2YFcxUB+HjOVrUOZB19ka78ndYDI1qF64aQByiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:57:46.642162Z","bundle_sha256":"b02d5e2f99dc40609ec2bb3caf39a04db07d245cf816062bb332c16c59472069"}}