{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PA63MDUKU2A4FKVJLU4UFXIHV5","short_pith_number":"pith:PA63MDUK","schema_version":"1.0","canonical_sha256":"783db60e8aa681c2aaa95d3942dd07af623828717e178d03a04ac570069b5a3b","source":{"kind":"arxiv","id":"1804.09140","version":1},"attestation_state":"computed","paper":{"title":"Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Massimo Pietroni","submitted_at":"2018-04-24T17:04:22Z","abstract_excerpt":"Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative series can be extended to a transseries including nonperturbative terms. The latter converges to the exact result well beyond the range of validity of perturbation theory. The crucial role of the divergences induced by shell-crossing is discussed. They provide constraints on the structure of the transseries and act as a bridge between the perturbative and t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.09140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2018-04-24T17:04:22Z","cross_cats_sorted":["hep-ph","hep-th"],"title_canon_sha256":"0e7d12477214f7907d2bf9f9fdb1df79317e0fe820f79b9aa69ea92b546d288c","abstract_canon_sha256":"3c938d855717f8b43cb431d2a87e3bfd96e76cfd0dcb78f7a317edd33af73110"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:49.284139Z","signature_b64":"N2cFfSKYbtOxWVRPXxQN8BRQuD6x3rhPIYMblgOJuO0GCCD+uuIg0w51unT/B1u3gsK+rOrlEB1g3wUAhbMGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"783db60e8aa681c2aaa95d3942dd07af623828717e178d03a04ac570069b5a3b","last_reissued_at":"2026-05-18T00:11:49.283418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:49.283418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Massimo Pietroni","submitted_at":"2018-04-24T17:04:22Z","abstract_excerpt":"Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative series can be extended to a transseries including nonperturbative terms. The latter converges to the exact result well beyond the range of validity of perturbation theory. The crucial role of the divergences induced by shell-crossing is discussed. They provide constraints on the structure of the transseries and act as a bridge between the perturbative and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09140","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.09140","created_at":"2026-05-18T00:11:49.283541+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.09140v1","created_at":"2026-05-18T00:11:49.283541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09140","created_at":"2026-05-18T00:11:49.283541+00:00"},{"alias_kind":"pith_short_12","alias_value":"PA63MDUKU2A4","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"PA63MDUKU2A4FKVJ","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"PA63MDUK","created_at":"2026-05-18T12:32:43.782077+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2301.09655","citing_title":"Perturbation-theory informed integrators for cosmological simulations","ref_index":80,"is_internal_anchor":true},{"citing_arxiv_id":"2509.18971","citing_title":"Post-collapse Lagrangian perturbation theory in three dimensions","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5","json":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5.json","graph_json":"https://pith.science/api/pith-number/PA63MDUKU2A4FKVJLU4UFXIHV5/graph.json","events_json":"https://pith.science/api/pith-number/PA63MDUKU2A4FKVJLU4UFXIHV5/events.json","paper":"https://pith.science/paper/PA63MDUK"},"agent_actions":{"view_html":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5","download_json":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5.json","view_paper":"https://pith.science/paper/PA63MDUK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.09140&json=true","fetch_graph":"https://pith.science/api/pith-number/PA63MDUKU2A4FKVJLU4UFXIHV5/graph.json","fetch_events":"https://pith.science/api/pith-number/PA63MDUKU2A4FKVJLU4UFXIHV5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5/action/storage_attestation","attest_author":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5/action/author_attestation","sign_citation":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5/action/citation_signature","submit_replication":"https://pith.science/pith/PA63MDUKU2A4FKVJLU4UFXIHV5/action/replication_record"}},"created_at":"2026-05-18T00:11:49.283541+00:00","updated_at":"2026-05-18T00:11:49.283541+00:00"}