{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:S6ASIYT5UO24GQFX6Q66UMWLEL","short_pith_number":"pith:S6ASIYT5","schema_version":"1.0","canonical_sha256":"978124627da3b5c340b7f43dea32cb22e8440daf969eb3aaf96fe26e217886c8","source":{"kind":"arxiv","id":"0801.3475","version":2},"attestation_state":"computed","paper":{"title":"Climbing a Legendrian mountain range without Stabilization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Douglas J. LaFountain, William W. Menasco","submitted_at":"2008-01-22T22:35:55Z","abstract_excerpt":"We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specific Legendrian and transversal MTWS by enhancing the Legendrian mountain range for the (2,3)-cable of a (2,3)-torus knot provided by Etnyre and Honda, and showing that elementary negative flypes allow us to move toward maximal tb value without having to use Legendrian stabilizatio"},"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":"0801.3475","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-01-22T22:35:55Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"8f247ea197e000b879d2bedf731533b676d1117521b2666c523e1f3bb94ad04a","abstract_canon_sha256":"8e89bd0742ec72c7cadf221df3b64c0112253a2748a823f6345115b8cc24a2a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:14.504719Z","signature_b64":"MIFWOFmwq4IH9VXPquVFKcGDWnOxvMYjXDYGDjmRNF7fsjIcKttA8ifnO5yBU0NWKj24E6CNSezmQkqNdNzSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"978124627da3b5c340b7f43dea32cb22e8440daf969eb3aaf96fe26e217886c8","last_reissued_at":"2026-05-18T01:46:14.504177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:14.504177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Climbing a Legendrian mountain range without Stabilization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Douglas J. LaFountain, William W. Menasco","submitted_at":"2008-01-22T22:35:55Z","abstract_excerpt":"We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specific Legendrian and transversal MTWS by enhancing the Legendrian mountain range for the (2,3)-cable of a (2,3)-torus knot provided by Etnyre and Honda, and showing that elementary negative flypes allow us to move toward maximal tb value without having to use Legendrian stabilizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3475","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":""},"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":"0801.3475","created_at":"2026-05-18T01:46:14.504261+00:00"},{"alias_kind":"arxiv_version","alias_value":"0801.3475v2","created_at":"2026-05-18T01:46:14.504261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3475","created_at":"2026-05-18T01:46:14.504261+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6ASIYT5UO24","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6ASIYT5UO24GQFX","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6ASIYT5","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL","json":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL.json","graph_json":"https://pith.science/api/pith-number/S6ASIYT5UO24GQFX6Q66UMWLEL/graph.json","events_json":"https://pith.science/api/pith-number/S6ASIYT5UO24GQFX6Q66UMWLEL/events.json","paper":"https://pith.science/paper/S6ASIYT5"},"agent_actions":{"view_html":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL","download_json":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL.json","view_paper":"https://pith.science/paper/S6ASIYT5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0801.3475&json=true","fetch_graph":"https://pith.science/api/pith-number/S6ASIYT5UO24GQFX6Q66UMWLEL/graph.json","fetch_events":"https://pith.science/api/pith-number/S6ASIYT5UO24GQFX6Q66UMWLEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL/action/storage_attestation","attest_author":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL/action/author_attestation","sign_citation":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL/action/citation_signature","submit_replication":"https://pith.science/pith/S6ASIYT5UO24GQFX6Q66UMWLEL/action/replication_record"}},"created_at":"2026-05-18T01:46:14.504261+00:00","updated_at":"2026-05-18T01:46:14.504261+00:00"}