{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:PBLI3HAJ4HGMO7IHYNJ3V3EZUR","short_pith_number":"pith:PBLI3HAJ","schema_version":"1.0","canonical_sha256":"78568d9c09e1ccc77d07c353baec99a45846400ae233f7adada4816dbd304d60","source":{"kind":"arxiv","id":"2208.11528","version":2},"attestation_state":"computed","paper":{"title":"Convergences of looptrees coded by excursions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Robin Khanfir","submitted_at":"2022-08-24T13:20:54Z","abstract_excerpt":"In order to study convergences of looptrees, we construct continuum trees and looptrees from real-valued c\\`adl\\`ag functions without negative jumps called excursions. We then provide a toolbox to manipulate the two resulting codings of metric spaces by excursions and we formalize the principle that jumps correspond to loops and that continuous growths correspond to branches. Combining these codings creates new metric spaces from excursions that we call vernation trees. They consist of a collection of loops and trees glued along a tree structure so that they unify trees and looptrees. We also "},"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":"2208.11528","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-08-24T13:20:54Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"3190981ec3e8c7eb7922e25d2fe6341fb748f60b2c19795aaa37d2676a937bfb","abstract_canon_sha256":"7e436d880071ab31125a59e3835eea782811b3b78219dbeed4ae2f7eaafd67a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:56.851832Z","signature_b64":"3uhlK5g0aNL27810J9i4VFYFf01cnGgHgLydDG2INhFM7Ce+45FzMBc/N/XOQTdeu39R/pfjb6/sQDQFcDPFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78568d9c09e1ccc77d07c353baec99a45846400ae233f7adada4816dbd304d60","last_reissued_at":"2026-07-05T12:06:56.851384Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:56.851384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergences of looptrees coded by excursions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Robin Khanfir","submitted_at":"2022-08-24T13:20:54Z","abstract_excerpt":"In order to study convergences of looptrees, we construct continuum trees and looptrees from real-valued c\\`adl\\`ag functions without negative jumps called excursions. We then provide a toolbox to manipulate the two resulting codings of metric spaces by excursions and we formalize the principle that jumps correspond to loops and that continuous growths correspond to branches. Combining these codings creates new metric spaces from excursions that we call vernation trees. They consist of a collection of loops and trees glued along a tree structure so that they unify trees and looptrees. We also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.11528","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.11528/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2208.11528","created_at":"2026-07-05T12:06:56.851442+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.11528v2","created_at":"2026-07-05T12:06:56.851442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.11528","created_at":"2026-07-05T12:06:56.851442+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBLI3HAJ4HGM","created_at":"2026-07-05T12:06:56.851442+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBLI3HAJ4HGMO7IH","created_at":"2026-07-05T12:06:56.851442+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBLI3HAJ","created_at":"2026-07-05T12:06:56.851442+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.21823","citing_title":"Discrete snakes with globally centered displacements","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR","json":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR.json","graph_json":"https://pith.science/api/pith-number/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/graph.json","events_json":"https://pith.science/api/pith-number/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/events.json","paper":"https://pith.science/paper/PBLI3HAJ"},"agent_actions":{"view_html":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR","download_json":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR.json","view_paper":"https://pith.science/paper/PBLI3HAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.11528&json=true","fetch_graph":"https://pith.science/api/pith-number/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/graph.json","fetch_events":"https://pith.science/api/pith-number/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/action/storage_attestation","attest_author":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/action/author_attestation","sign_citation":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/action/citation_signature","submit_replication":"https://pith.science/pith/PBLI3HAJ4HGMO7IHYNJ3V3EZUR/action/replication_record"}},"created_at":"2026-07-05T12:06:56.851442+00:00","updated_at":"2026-07-05T12:06:56.851442+00:00"}