{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:Q7J25WZUJKQMYTZG65KDZXTRWE","short_pith_number":"pith:Q7J25WZU","canonical_record":{"source":{"id":"1002.1676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-08T17:58:18Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"4330daa9a37a5edc0a97c8c0d0f110ff66fc7e82ef0f79da66072e1f50a9585b","abstract_canon_sha256":"f99b34964a4b9c07b836b2ee66647fe3b5816b3cef1deb65c8c31a516c697028"},"schema_version":"1.0"},"canonical_sha256":"87d3aedb344aa0cc4f26f7543cde71b108a09d385c478c03030dba1aed41a1c0","source":{"kind":"arxiv","id":"1002.1676","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1676","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1676v1","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1676","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"Q7J25WZUJKQM","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"Q7J25WZUJKQMYTZG","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"Q7J25WZU","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:Q7J25WZUJKQMYTZG65KDZXTRWE","target":"record","payload":{"canonical_record":{"source":{"id":"1002.1676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-08T17:58:18Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"4330daa9a37a5edc0a97c8c0d0f110ff66fc7e82ef0f79da66072e1f50a9585b","abstract_canon_sha256":"f99b34964a4b9c07b836b2ee66647fe3b5816b3cef1deb65c8c31a516c697028"},"schema_version":"1.0"},"canonical_sha256":"87d3aedb344aa0cc4f26f7543cde71b108a09d385c478c03030dba1aed41a1c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:16.201735Z","signature_b64":"jNtpI7XT/tHmicmcEAS7P4UCZhhDKIeGRFQPEJ2dNF4TtVljsxImFC8YFKMSqaAZHmnjhRbYwi0LgfvxeCqZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87d3aedb344aa0cc4f26f7543cde71b108a09d385c478c03030dba1aed41a1c0","last_reissued_at":"2026-05-18T04:13:16.201074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:16.201074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.1676","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":"2026-05-18T04:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AytPhqzQ3vyn3Yo2bY41LB0B040pJcZjKxWGxGIAPFRaM7L/nbwEH+X0HSRK7UsBTFf82jPqX1D4v5WIS7sZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:03:34.203760Z"},"content_sha256":"fc4e734d765a26007fe9ec8e45ae42289edf2c707a99b1ab7c55200f10d6c66d","schema_version":"1.0","event_id":"sha256:fc4e734d765a26007fe9ec8e45ae42289edf2c707a99b1ab7c55200f10d6c66d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:Q7J25WZUJKQMYTZG65KDZXTRWE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformations of bordered Riemann surfaces and associahedral polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.AG","authors_text":"Cid Vipismakul, Satyan L. Devadoss, Timothy Heath","submitted_at":"2010-02-08T17:58:18Z","abstract_excerpt":"We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling. Our main result classifies all such spaces that can be realized as convex polytopes. A new polytope is introduced based on truncations of cubes, and its combinatorial and algebraic structure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1676","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":"2026-05-18T04:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G04tdzicYs/92nd/GRVVH/FcR1VylYVfBAThEUKymEQsB6+2WbnkcArq1ZMxcUUKEIqvTO8Zuy6+xOxzx8CMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:03:34.204475Z"},"content_sha256":"d2c87d6bfb5635689c703f2088a02cdd9e2b65c850c900ee7644965535b04539","schema_version":"1.0","event_id":"sha256:d2c87d6bfb5635689c703f2088a02cdd9e2b65c850c900ee7644965535b04539"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7J25WZUJKQMYTZG65KDZXTRWE/bundle.json","state_url":"https://pith.science/pith/Q7J25WZUJKQMYTZG65KDZXTRWE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7J25WZUJKQMYTZG65KDZXTRWE/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":"2026-05-29T17:03:34Z","links":{"resolver":"https://pith.science/pith/Q7J25WZUJKQMYTZG65KDZXTRWE","bundle":"https://pith.science/pith/Q7J25WZUJKQMYTZG65KDZXTRWE/bundle.json","state":"https://pith.science/pith/Q7J25WZUJKQMYTZG65KDZXTRWE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7J25WZUJKQMYTZG65KDZXTRWE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Q7J25WZUJKQMYTZG65KDZXTRWE","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":"f99b34964a4b9c07b836b2ee66647fe3b5816b3cef1deb65c8c31a516c697028","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-08T17:58:18Z","title_canon_sha256":"4330daa9a37a5edc0a97c8c0d0f110ff66fc7e82ef0f79da66072e1f50a9585b"},"schema_version":"1.0","source":{"id":"1002.1676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1676","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1676v1","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1676","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"Q7J25WZUJKQM","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"Q7J25WZUJKQMYTZG","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"Q7J25WZU","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:d2c87d6bfb5635689c703f2088a02cdd9e2b65c850c900ee7644965535b04539","target":"graph","created_at":"2026-05-18T04:13:16Z","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 consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling. Our main result classifies all such spaces that can be realized as convex polytopes. A new polytope is introduced based on truncations of cubes, and its combinatorial and algebraic structure","authors_text":"Cid Vipismakul, Satyan L. Devadoss, Timothy Heath","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-08T17:58:18Z","title":"Deformations of bordered Riemann surfaces and associahedral polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1676","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:fc4e734d765a26007fe9ec8e45ae42289edf2c707a99b1ab7c55200f10d6c66d","target":"record","created_at":"2026-05-18T04:13:16Z","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":"f99b34964a4b9c07b836b2ee66647fe3b5816b3cef1deb65c8c31a516c697028","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-08T17:58:18Z","title_canon_sha256":"4330daa9a37a5edc0a97c8c0d0f110ff66fc7e82ef0f79da66072e1f50a9585b"},"schema_version":"1.0","source":{"id":"1002.1676","kind":"arxiv","version":1}},"canonical_sha256":"87d3aedb344aa0cc4f26f7543cde71b108a09d385c478c03030dba1aed41a1c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87d3aedb344aa0cc4f26f7543cde71b108a09d385c478c03030dba1aed41a1c0","first_computed_at":"2026-05-18T04:13:16.201074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:16.201074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jNtpI7XT/tHmicmcEAS7P4UCZhhDKIeGRFQPEJ2dNF4TtVljsxImFC8YFKMSqaAZHmnjhRbYwi0LgfvxeCqZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:16.201735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc4e734d765a26007fe9ec8e45ae42289edf2c707a99b1ab7c55200f10d6c66d","sha256:d2c87d6bfb5635689c703f2088a02cdd9e2b65c850c900ee7644965535b04539"],"state_sha256":"47ff369780e1f9b2f9b89fb39c434564fa7cc48027d6a94abd2e8adc09efa0b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWOeWozRMfac/2xsKb8P8AfePexf6DkdW2RONmBVeMob2dwCxkfwEiLbySNhk2SgX9bpsms1+3MTf+JRLZdiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:03:34.207887Z","bundle_sha256":"80a52858bfc132284a804dc63aa767b3500dbe4e946a05972f44543cd8f6ab53"}}