{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TFY7N5VUQPA64RHRPVX4WJPWJL","short_pith_number":"pith:TFY7N5VU","canonical_record":{"source":{"id":"1207.3073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-12T19:47:33Z","cross_cats_sorted":[],"title_canon_sha256":"5585969df789248fa5e223db1d7952a69aaedc6654ab1c98c6a65af3d2be2ea0","abstract_canon_sha256":"f8302ce5661fd87c34e4df88f97bcc6cec1e27da7aea86a792cbc291ab63b7b4"},"schema_version":"1.0"},"canonical_sha256":"9971f6f6b483c1ee44f17d6fcb25f64ae8d58fac8a0e6e93cc3f9633b484195f","source":{"kind":"arxiv","id":"1207.3073","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3073","created_at":"2026-05-18T03:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3073v2","created_at":"2026-05-18T03:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3073","created_at":"2026-05-18T03:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"TFY7N5VUQPA6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TFY7N5VUQPA64RHR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TFY7N5VU","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TFY7N5VUQPA64RHRPVX4WJPWJL","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-12T19:47:33Z","cross_cats_sorted":[],"title_canon_sha256":"5585969df789248fa5e223db1d7952a69aaedc6654ab1c98c6a65af3d2be2ea0","abstract_canon_sha256":"f8302ce5661fd87c34e4df88f97bcc6cec1e27da7aea86a792cbc291ab63b7b4"},"schema_version":"1.0"},"canonical_sha256":"9971f6f6b483c1ee44f17d6fcb25f64ae8d58fac8a0e6e93cc3f9633b484195f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:27.900269Z","signature_b64":"c5KpoLAvkUVGSDe653q3cwyVIwW1fTz9DjFie+3vveMQGCwoFUzaO7N2p3guJM1+Um0xio7GA5VXU42PKSYNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9971f6f6b483c1ee44f17d6fcb25f64ae8d58fac8a0e6e93cc3f9633b484195f","last_reissued_at":"2026-05-18T03:22:27.899450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:27.899450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3073","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yxdiOoL8reKLM+C//yIYgP0YNXXU0Hv+4gg39xwbRaiktJeJ5X+HCZ4HqxRvTlt0mh6PtVCBBqSlrKxugUWNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:40:46.787402Z"},"content_sha256":"8a7232eb895b7efc7ffb28f4df3f2a3b86cf3eb2add2a86cdb341e4ffb27aaa3","schema_version":"1.0","event_id":"sha256:8a7232eb895b7efc7ffb28f4df3f2a3b86cf3eb2add2a86cdb341e4ffb27aaa3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TFY7N5VUQPA64RHRPVX4WJPWJL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"General Form of $s$, $t$, $u$ Symmetric Polynomial and Heavy Quarkonium physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Yan-Qing Ma","submitted_at":"2012-07-12T19:47:33Z","abstract_excerpt":"Induced by three gluons symmetry, Mandelstam variables $s$, $t$, $u$ symmetric expressions are widely involved in collider physics, especially in heavy quarkonium physics. In this work we study general form of $s$, $t$, $u$ symmetric polynomials, and find that they can be expressed as polynomials where the symmetry is manifest. The general form is then used to simplify expressions which asymptotically reduces the length of original expression to one-sixth. Based on the general form, we reproduce the exact differential cross section of $J/\\psi$ hadron production at leading order in $v^2$ up to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3073","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNAy+n865iZyg94FiSqmIFmitNtZc44zm0SoTjW6Nx8V2onjzxPmYxsGP1JZxNnMPUeAz4BK3KsE/RmMwFoRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:40:46.787879Z"},"content_sha256":"340375bc84f18a2e0ba340a55ecd49715e4bfba0dcbdd63407c01c4d9eefcb6d","schema_version":"1.0","event_id":"sha256:340375bc84f18a2e0ba340a55ecd49715e4bfba0dcbdd63407c01c4d9eefcb6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TFY7N5VUQPA64RHRPVX4WJPWJL/bundle.json","state_url":"https://pith.science/pith/TFY7N5VUQPA64RHRPVX4WJPWJL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TFY7N5VUQPA64RHRPVX4WJPWJL/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":"2026-08-19T18:40:46Z","links":{"resolver":"https://pith.science/pith/TFY7N5VUQPA64RHRPVX4WJPWJL","bundle":"https://pith.science/pith/TFY7N5VUQPA64RHRPVX4WJPWJL/bundle.json","state":"https://pith.science/pith/TFY7N5VUQPA64RHRPVX4WJPWJL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TFY7N5VUQPA64RHRPVX4WJPWJL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TFY7N5VUQPA64RHRPVX4WJPWJL","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":"f8302ce5661fd87c34e4df88f97bcc6cec1e27da7aea86a792cbc291ab63b7b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-12T19:47:33Z","title_canon_sha256":"5585969df789248fa5e223db1d7952a69aaedc6654ab1c98c6a65af3d2be2ea0"},"schema_version":"1.0","source":{"id":"1207.3073","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3073","created_at":"2026-05-18T03:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3073v2","created_at":"2026-05-18T03:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3073","created_at":"2026-05-18T03:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"TFY7N5VUQPA6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TFY7N5VUQPA64RHR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TFY7N5VU","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:340375bc84f18a2e0ba340a55ecd49715e4bfba0dcbdd63407c01c4d9eefcb6d","target":"graph","created_at":"2026-05-18T03:22:27Z","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":"Induced by three gluons symmetry, Mandelstam variables $s$, $t$, $u$ symmetric expressions are widely involved in collider physics, especially in heavy quarkonium physics. In this work we study general form of $s$, $t$, $u$ symmetric polynomials, and find that they can be expressed as polynomials where the symmetry is manifest. The general form is then used to simplify expressions which asymptotically reduces the length of original expression to one-sixth. Based on the general form, we reproduce the exact differential cross section of $J/\\psi$ hadron production at leading order in $v^2$ up to ","authors_text":"Yan-Qing Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-12T19:47:33Z","title":"General Form of $s$, $t$, $u$ Symmetric Polynomial and Heavy Quarkonium physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3073","kind":"arxiv","version":2},"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":"sha256:8a7232eb895b7efc7ffb28f4df3f2a3b86cf3eb2add2a86cdb341e4ffb27aaa3","target":"record","created_at":"2026-05-18T03:22:27Z","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":"f8302ce5661fd87c34e4df88f97bcc6cec1e27da7aea86a792cbc291ab63b7b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-12T19:47:33Z","title_canon_sha256":"5585969df789248fa5e223db1d7952a69aaedc6654ab1c98c6a65af3d2be2ea0"},"schema_version":"1.0","source":{"id":"1207.3073","kind":"arxiv","version":2}},"canonical_sha256":"9971f6f6b483c1ee44f17d6fcb25f64ae8d58fac8a0e6e93cc3f9633b484195f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9971f6f6b483c1ee44f17d6fcb25f64ae8d58fac8a0e6e93cc3f9633b484195f","first_computed_at":"2026-05-18T03:22:27.899450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:27.899450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c5KpoLAvkUVGSDe653q3cwyVIwW1fTz9DjFie+3vveMQGCwoFUzaO7N2p3guJM1+Um0xio7GA5VXU42PKSYNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:27.900269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3073","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a7232eb895b7efc7ffb28f4df3f2a3b86cf3eb2add2a86cdb341e4ffb27aaa3","sha256:340375bc84f18a2e0ba340a55ecd49715e4bfba0dcbdd63407c01c4d9eefcb6d"],"state_sha256":"d3adfa967091b726cc33c102bd38972f2ad1caf6e28f42eddde1cea342949d3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8GG9TSeVr8hpsqs+yb6HBUVjEJb4OFoR52fXRX5GXJ+hA/kaiyJgFP36QPYzZyOAKhg+AO+ic6uvLxrS5TE2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T18:40:46.792326Z","bundle_sha256":"c3722215009068be182209ccf03e4ebeb8868c3a6a451ab5eaf3727a2a8d842c"}}